If a crime cannot be committed without also committing a lesser offense, is the latter included within the former?

If a crime cannot be committed without also committing a lesser offense, the latter is a lesser included offense within the former. (People v. Lopez (1998) 19 Cal.4th 282, 288.) "We have applied two tests in determining whether an uncharged offense is necessarily included within a charged offense: the `elements test' and the `accusatory pleading' test. Under the elements test, if the statutory elements of the greater offense include all of the statutory elements of the lesser offense, the latter is necessarily included in the former. Under the accusatory pleading test, if the facts actually alleged in the accusatory pleading include all of the elements of the lesser offense, the latter is necessarily included in the former. [Citation.]" (People v. Reed (2006) 38 Cal.4th 1224, 1227.) Both parties agree the elements test, and not the accusatory pleading test should be applied.