GANTS, J.

On the evening of March 29, 2006, the defendant, a special agent with the office of export enforcement of the United States Department of Commerce, was driving on Congress Street in Boston on his way home from work. Viewed in the light most favorable to the prosecution, the evidence at trial showed that, after the defendant took a right turn onto Dorchester Avenue, the victim rode up to the defendant's passenger side window on his motorcycle to complain that the defendant had nearly hit his friend, who was also driving a motorcycle. The defendant swore at the victim and claimed that the victim's friend had cut him off.

The verbal altercation between the defendant and the victim continued over several blocks. The two men turned left onto Summer Street and drove on, at times side by side, with the victim's motorcycle in the left lane and the defendant's vehicle in the right lane. At one point the defendant's vehicle swerved so close to the victim's motorcycle that the victim warned the defendant not to come any closer. The defendant responded by pointing a gun at the victim, and the victim taunted, "What are you going to do, shoot me?" Soon after, the defendant swerved his vehicle again, this time striking the victim's motorcycle and sending the victim flying through the air, causing him serious bodily injury.

The jury were instructed on each of the three indictments, charging the defendant with assault and battery by means of a dangerous weapon (an automobile) and causing serious bodily injury, in violation of G.L. c. 265, § 15A ; assault by means of a dangerous weapon (a handgun), in violation of G.L. c. 265, § 15B (b); and leaving the scene of an accident causing personal injury, in violation of G.L. c. 90, § 24 (2) (a ½) (1). After two days of deliberation, the jury informed the judge that they were "hopelessly deadlocked" on the first indictment but had reached verdicts on the others. The jury returned their verdicts, finding the defendant not guilty on the second indictment and guilty on the third, and the judge then provided them with standard instructions to help them resolve their deadlock. See Commonwealth v. Rodriquez, 364 Mass. 87, 101-102 (1973) (Appendix A).

After further deliberations, the jury asked the judge if they could consider the charge of assault by means of a dangerous weapon (an automobile). Over the defendant's objection, the judge instructed the jury that they could consider that offense because it was a lesser included charge within the indictment. The jury then found the defendant guilty of assault by means of a dangerous weapon.

The Appeals Court affirmed the judgment of conviction of leaving the scene of an accident causing personal injury, but reversed the judgment of conviction of assault by means of a dangerous weapon and set aside the verdict. Commonwealth v. Porro, 74 Mass. App. Ct. 676, 684-685 (2009). The court held that, because there was evidence at trial of more than one swerve of the defendant's vehicle and the judge had refused to instruct the jury that the indictment charged only the final swerve that resulted in the victim's injury, there remained "a substantial risk that the defendant was convicted of a crime for which he was not indicted by a grand jury." Id. at 682, quoting Commonwealth v. Barbosa, 471 Mass. 547, 554 (1995). The court also held that the Commonwealth could not retry the defendant on the charge of aggravated assault and battery by means of a dangerous weapon, because the jury's conviction on the lesser included charge was an implied acquittal of the greater charge; the court allowed the defendant to be retried on the lesser included charge of assault by means of a dangerous weapon under an attempted battery theory. Id.

We granted the defendant's application for further appellate review but limited our review to the issue whether the defendant can be retried for assault by means of a dangerous weapon. We conclude that the defendant may be retried for assault by means of a dangerous weapon as to the final swerve, but only under a threatened battery theory, not under an attempted battery theory. Discussion. To determine how our jurisprudence regarding lesser included offenses applies to the crimes of assault and assault and battery, we need first to examine the various alternative theories by which these crimes may be proved.

1. Assault versus assault and battery. The punishments for the crimes of assault and assault and battery, by means of a dangerous weapon (or without), are established by statute, but the elements necessary to convict a person of these crimes are determined by the common law. See Commonwealth v. Gorassi, 432 Mass. 244, 247 (2000); Commonwealth v. Burke, 390 Mass. 480, 482 (1983); G.L. c. 265, § 13A (assault or assault and battery); G.L. c. 265, § 15A (assault and battery by means of a dangerous weapon, and aggravated forms of that crime); G.L. c. 265, § 15B (assault by means of a dangerous weapon). See also Commonwealth v. Stokes, 440 Mass. 741, 747 (2004), quoting Commonwealth v. Burke, 392 Mass. 688, 690 (1984) ("Where the Legislature does not define a term, we presume that its intent is to incorporate the common-law definition of that term, 'unless the intent to alter it is clearly expressed'").

Under the common law, there are two theories of assault and battery: intentional battery and reckless battery. Commonwealth v. Burno, 396 Mass. 622, 625 (1986). An intentional assault and battery is "the intentional and unjustified use of force upon the person of another, however slight." Commonwealth v. McCan, 277 Mass. 199, 203 (1931). See Commonwealth v. Moore, 36 Mass. App. Ct. 455, 459 (1994) (assault and battery involves touching that is intentional, not simply result of intentional act). Where the touching is physically harmful, "consent is immaterial," but "a nonharmful touching is a battery only if there is no consent." Commonwealth v. Burke, 390 Mass. at 481. A reckless assault and battery is committed when an individual engages in reckless conduct that results in a touching producing physical injury to another person; an unconsented touching is not sufficient. Commonwealth v. Burno, supra. Commonwealth v. Correia, 50 Mass. App. Ct. 455, 456, 458 (2000). Commonwealth v. Welch, 16 Mass. App. Ct. 271, 275-276 (1983). Under both theories of battery, the "touching may be . . . indirect, as by setting in motion some force or instrumentality" that causes the victim to be touched, such as where a defendant fires a gunshot that strikes the victim or intentionally or recklessly drives his vehicle into a vehicle occupied by the victim. Commonwealth v. Dixon, 34 Mass. App. Ct. 653, 654 (1993). See Commonwealth v. Burno, supra at 628 ("a battery could occur although no force was applied to a person directly"); Commonwealth v. Stratton, 114 Mass. 303, 305-306 (1873).

At trial in this case, the prosecution alleged that the defendant intentionally struck the victim's motorcycle with his vehicle, and the jury were instructed on the intentional form of assault and battery. Although there was evidence at trial sufficient to support a conviction on a reckless battery theory, the prosecution did not ask that the jury be instructed on this theory, and no instruction was given.

There are also two theories of assault under the common law: attempted battery and threatened battery. See Commonwealth v. Richards, 363 Mass. 299, 303 (1973). A conviction of assault under a theory of attempted battery requires the prosecution to prove that the defendant "intended to commit a battery, took some overt step toward accomplishing that intended battery, and came reasonably close to doing so." Commonwealth v. Melton, 436 Mass. 291, 295 (2002). The prosecution need not prove that the victim was aware of the attempted battery (e.g., the victim could be unconscious or have his back turned when the attempted battery occurred). See Commonwealth v. Gorassi, supra at 248.

A conviction of assault under a theory of threatened battery requires the prosecution to prove that the defendant engaged in conduct that a reasonable person would recognize to be threatening, that the defendant intended to place the victim in fear of an imminent battery, and that the victim perceived the threat. See Commonwealth v. Chambers, 57 Mass. App. Ct. 47, 49, 51 (2003); Commonwealth v. Musgrave, 38 Mass. App. Ct. 519, 523-524 (1995), S.C., 421 Mass. 610 (1996) (adopting opinion of Appeals Court). The victim need not actually be in fear but must apprehend the risk of an imminent battery. Commonwealth v. Chambers, supra at 49-51.

An assault under a theory of attempted battery, therefore, has elements different from an assault under a theory of threatened battery. A defendant must intend a battery to be guilty under the attempted battery theory, but a defendant need not intend to strike the victim to be guilty under the threatened battery theory; it is sufficient that a defendant engages in menacing conduct that would place a reasonable person in fear of being struck, that the defendant intends by this conduct to place the victim in fear of an imminent battery, and that the victim recognizes the conduct to be threatening an imminent battery.

2. Lesser included offenses. Because the judge in this case allowed the jury to consider both the attempted battery and the threatened battery theory of assault as lesser included offenses of intentional assault and battery, we must determine whether these instructions complied with our jurisprudence of lesser included offenses. Under our long-standing rule derived from Morey v. Commonwealth, 108 Mass. 433, 434 (1871), a lesser included offense is one whose elements are a subset of the elements of the charged offense. See Commonwealth v. Jones, 382 Mass. 387, 393 (1981). Thus, a "lesser included offense is one which is necessarily accomplished on commission of the greater crime." Commonwealth v. D'Amour, 428 Mass. 725, 748 (1999).

The determination that an offense is a lesser included offense has two significant consequences. First, double jeopardy prohibits a defendant from being convicted and, therefore, sentenced, for both the greater and lesser offense as a result of the same act. See Commonwealth v. Vick, 454 Mass. 418, 431-433 (2009); Commonwealth v. Ogden O., 448 Mass. 798, 808 (2007). In contrast, where "each offense requires proof of an additional element that the other does not, 'neither crime is a lesser-included offense of the other, and the convictions on both are deemed to have been authorized by the Legislature and hence not [duplicative].'" Commonwealth v. Vick, supra at 431, quoting Commonwealth v. Jones, supra at 393. Where the elements differ, even if the two offenses arise from the same conduct, the defendant may be convicted of and sentenced on both offenses, and the sentence on one offense may begin on and after the completion of the sentence on the other offense. Commonwealth v. Vick, supra at 431, 436.

Second, where one offense is a lesser included offense, a single indictment for the greater offense allows a jury to be instructed on and to consider any lesser included offenses for which the evidence may support a conviction. See Commonwealth v. Walker, 426 Mass. 301, 303 (1997); Commonwealth v. Perry, 391 Mass. 808, 809, 813-814 (1984). See also Commonwealth v. Gagnon, 387 Mass. 768, 769 (1982), cert. denied, 461 U.S. 921 and 464 U.S. 815 (1983). Lesser included offenses serve an important purpose by "allowing the jury to convict of the offense established by the evidence, rather than forcing them to choose between convicting the defendant of an offense not fully established by the evidence or acquitting, even though the defendant is guilty of some offense." Commonwealth v. Woodward, 427 Mass. 659, 664-665 (1998).

Although we have repeatedly reaffirmed the elements-based approach to lesser included offenses, see, e.g., Commonwealth v. Pimental, 454 Mass. 475, 482 (2009), we have recognized rare circumstances where the purposes of our lesser included offense jurisprudence are not served by a strict application of the doctrine in a particular case. See Commonwealth v. Walker, supra at 305; Costarelli v. Commonwealth, 374 Mass. 677, 684 (1978). In general, the cases where we have diverged from a strict application of the Morey rule have involved instances where, although each offense contains an element that the other does not, the different element in the lesser included offense is routinely undisputed and was not in dispute in the particular case.

In Commonwealth v. Walker, supra at 301-302, a defendant charged with the rape of two six year old children was convicted of indecent assault and battery on a child under the age of fourteen. We affirmed the convictions, concluding that indecent assault and battery on a child under fourteen years of age is a lesser included offense of forcible rape of a child under the age of sixteen, even though the element regarding the victim's age differs between the two offenses and the indictments did not allege that the victims were under fourteen. Id. at 305-306. See Commonwealth v. King, 445 Mass. 217, 225 (2005), cert. denied, 546 U.S. 1216 (2006). We concluded that, where there was no dispute as to the age of the victims, adherence to the strict elements approach to lesser included offenses in the Walker case was contrary to the underlying purpose of the doctrine because, where the jury were convinced there was indecent touching but were uncertain whether penetration had been proven beyond a reasonable doubt, they should not be required to choose between convicting the defendant of rapes that had not been proven or acquitting a defendant who had sexually assaulted young children. See Commonwealth v. Walker, supra at 304-305.

In Costarelli v. Commonwealth, supra at 683-684, we concluded that unauthorized use of a motor vehicle was a lesser included offense of larceny of a motor vehicle, even though the lesser offense included an element, use on a public way, that was not required for conviction of the greater offense. We noted that, in practice, this element would not often be contested, and that "the characterization of use without authority as a lesser included offense of larceny is in accord with the realities of the offenses and the circumstances within which they occur." Id. at 684. See Commonwealth v. D'Amour, supra at 748-749 (conspiracy is lesser included offense of accessory before fact to murder where accessory charge is based on theory that defendant hired killer).

This case requires us to determine whether each theory of assault is a lesser included offense of assault and battery. The attempted battery theory of assault is clearly a lesser included offense of intentional assault and battery; the elements are the same except that intentional assault and battery contains the additional element that the battery be completed by an actual touching of the victim. The threatened battery theory of assault, however, contains elements not found in either theory of assault and battery, the intent to place the victim in fear of an imminent battery, Commonwealth v. Musgrave, 38 Mass. App. Ct. 519, 523-525 (1995); and the victim's actual apprehension, or awareness, of the threat. See Commonwealth v. Chambers, 57 Mass. App. Ct. 47, 51 (2003).

While it does not fit neatly into our elements-based definition of a lesser included offense, we conclude that the threatened battery theory of assault is a lesser included offense of intentional assault and battery. The elements in threatened battery are generally incidental to an intentional assault and battery: the defendant will usually intend to put the victim in fear and the victim will usually recognize the threat posed by the imminent battery. Because attempted battery and threatened battery "are closely related," Commonwealth v. Santos, 440 Mass. 281, 289 (2003), we do not require that a jury be unanimous as to which theory of assault forms the basis for their verdict; a jury may find a defendant guilty of assault if some jurors find the defendant committed an attempted battery (because they are convinced the defendant intended to strike the victim and missed) and the remainder find that he committed a threatened battery (because they are convinced that the defendant intended to frighten the victim by threatening an assault). See id. at 284, 289 (jury were not required to be unanimous as to which form of assault was relied on to satisfy assault element of armed robbery). This same close relation dictates that, just as attempted battery assault is a lesser included offense of intentional assault and battery, so, too, is threatened battery assault.

We have long recognized the Morey rule as a doctrine that respects the Legislature's role as "the primary body that creates, and defines, crimes." Commonwealth v. Jones, 441 Mass. 73, 75 (2004). See Commonwealth v. Vick, 454 Mass. 418, 431-432 (2009). Our decision that a defendant charged with assault and battery faces a single conviction under either theory of assault and battery or either theory of assault is consistent with the Legislature's statutory grouping of these common-law offenses. See G.L. c. 265, § 13A (a) ("Whoever commits an assault or an assault and battery upon another shall be punished . . ."). If we were to conclude that assault under a theory of threatened battery was not a lesser included offense of intentional battery, a prosecutor could charge a defendant with both assault and assault and battery, a jury could convict the defendant of both assault and battery and assault under a theory of threatened battery, and a judge could impose an "on and after" sentence on the assault conviction, thus securing a greater penalty than that established by the Legislature. A jury considering these charges as separate and distinct crimes would need to reach separate verdicts, even though, if only assault had been charged, they could not render a separate verdict of attempted battery and threatened battery. See Commonwealth v. Santos, supra at 289. If the prosecutor charged the defendant only with assault and battery and did not separately charge assault, a jury would be required to acquit a defendant if they could not conclude beyond a reasonable doubt that the defendant intended to touch rather than simply scare the victim. The jury, then, would not be spared from having to choose between convicting the defendant of an offense not fully established by the evidence, or finding the defendant not guilty of any crime even where they conclude that the defendant is guilty of a related, less serious offense. See Commonwealth v. Woodward, ATI Mass. 659, 664-665 (1998); Commonwealth v. Walker, 426 Mass. 301, 305 (1997).

The defendant cannot fairly contend that he did not receive fair notice that an assault and battery charge includes a charge of assault under a theory of threatened battery. Our common law has long recognized two theories of assault, see Commonwealth v. White, 110 Mass. 407, 409 (1872), and courts have assumed, without deciding, that both forms of assault were lesser included offenses of assault and battery. See, e.g., Commonwealth v. Chambers, supra at 48 n. 1.

3. Lesser included offense instruction. Having concluded that both theories of assault are lesser included offenses of intentional assault and battery, we now turn to the question whether, based on the evidence at trial, the judge erred in allowing the jury to consider both theories of assault. Our case law on lesser included offense instructions has consistently inquired "whether the evidence at trial presents 'a rational basis for acquitting the defendant of the crime charged and convicting him of the lesser included offense. '" Commonwealth v. Donlan, 436 Mass. 329, 335 (2002), quoting Commonwealth v. Drewnowski, 44 Mass. App. Ct. 687, 692 (1998). See Commonwealth v. Linton, 456 Mass. 534, 552 (2010) (whether "any reasonable view of the evidence" supports conviction of lesser included but not greater offense).

In a typical case, the issue is posed in the context of a defendant who was convicted of the greater offense and claims that the judge erred in failing to give a requested lesser included offense instruction or that counsel was ineffective in failing to ask for such an instruction. See, e.g., id.; Commonwealth v. Staines, 441 Mass. 521, 537 (2004); Commonwealth v. Campbell, 352 Mass. 387, 391-392 (1967). In these cases, we have concluded that a defendant's entitlement to a lesser included offense instruction depends not only on the existence of a possible factual scenario justifying a conviction of the lesser but not the greater offense, but also on evidence of a dispute at trial about the element that distinguishes the two offenses. See Commonwealth v. Staines, supra at 538; Commonwealth v. Donlan, supra at 336-338. "[T]here must be 'some evidence on the element differentiating the greater and lesser offenses, '"that is, some evidence that specifically puts in question an element of the greater offense that is not required of the lesser offense. Id. at 336-337, quoting Commonwealth v. Egerton, 396 Mass. 499, 505 (1986). The "some evidence" that is required, "in ordinary circumstances, cannot be the mere possibility that the jury might not credit a portion of the Commonwealth's evidence." Commonwealth v. Donlan, supra at 337. "The judge need not reconstruct all possible factual scenarios subsumed in the evidence presented, no matter how unreasonable, and charge the jury accordingly." Id., quoting Commonwealth v. Egerton, supra.

Less typically, the issue is posed where a defendant is convicted of the lesser included offense and claims that the judge erred in allowing the jury to consider that offense. See Commonwealth v. Thayer, 418 Mass. 130, 133 (1994). In such cases, the question is not whether a judge was required to grant a request for a lesser included instruction, but whether such an instruction was permissible. Where there is no evidence to justify a lesser included instruction, that is, no evidence that would permit the jury to convict the defendant of the lesser included offense rather than the greater offense, we have concluded that it is reversible error to allow the jury to convict the defendant of the lesser charge. Commonwealth v. Nardone, 406 Mass. 123, 130 (1989). Without saying so, we have applied a slightly different test where the issue is whether the judge erred in giving a lesser included instruction rather than whether the judge erred by failing to give such an instruction: it is not error to give a lesser included offense instruction "if on any hypothesis of the evidence, the jury could have found the defendant[] guilty of [the lesser included offense]" and not guilty of the greater offense. Commonwealth v. Thayer, supra at 132. In determining whether there was a hypothetical basis for the jury to conclude that the defendant was guilty of the lesser included offense, but not the offense charged, the judge may consider the possibility that the jury reasonably may disbelieve the witnesses' testimony regarding an element required of the greater, but not the lesser included, offense. Id. at 133. It is therefore not impermissible for a judge to give an instruction on a lesser included offense even though the element that distinguishes the two offenses was not specifically disputed or put in issue at trial.

This case, like Commonwealth v. Thayer, supra, requires us to decide whether it was error for the judge to give a lesser included instruction, specifically, the instruction on the two forms of assault. With attempted battery assault, the only element that distinguishes it from intentional assault and battery is the actual touching of the victim by the defendant. On review of the record, we agree with the defendant that there was no reasonable hypothetical basis for the jury to believe that the defendant had attempted, but failed, to strike the victim or his motorcycle with his vehicle. The fact of the collision was not in dispute, and the defendant even stipulated that the victim suffered serious bodily injury. Because the jury could not reasonably have found the defendant not guilty of aggravated assault and battery by means of a dangerous weapon but guilty of assault by means of a dangerous weapon under an attempted battery theory, the judge erred in giving the lesser included instruction on that theory. See Commonwealth v. Nardone, supra.

The jury, however, reasonably could have found the defendant guilty of threatened battery assault but not guilty of the intentional assault and battery charged. The evidence permitted the jury reasonably to conclude that they had a reasonable doubt whether the defendant intended to strike the victim or his motorcycle, but no doubt that he at least intended to scare the victim by swerving close to him. While the defendant, who testified in his own defense, stated that he did not know the victim was to his left when he swerved, and no attorney in closing argument claimed that the defendant meant to scare the victim, a jury reasonably could have reached this conclusion from the circumstantial evidence admitted at trial.

Because a lesser included instruction as to the offense of assault by means of a dangerous weapon based on a theory of threatened battery, but not attempted battery, was warranted by the evidence at trial, the defendant may be retried on this theory alone, limited to the defendant's final swerve, which resulted in contact with the victim.

Conclusion. The defendant's conviction of assault by means of a dangerous weapon is reversed and the verdict is set aside. The case is remanded to the Superior Court. For the reasons discussed above, we conclude that the defendant may be retried for assault by means of a dangerous weapon on a threatened battery theory of assault only.

So ordered.