Old English crammian "press something into something else," from Proto-Germanic *kram-/*krem- (cognates: Old High German krimman "to press, pinch," Old Norse kremja "to squeeze, pinch"), from PIE root *ger- "to gather" (see gregarious). Meaning "study intensely for an exam" originally was British student slang first recorded 1803. Related: Crammed; cramming.
1928, U.S. slang, either a shortened form of scramble (v.) or from German schramm, imperative singular of schrammen "depart." Related: Scrammed; scramming.