Let and be elements of a commutative ring . A common multiple of and is an element of such that both and divide (that is, there exist elements and of such that and ). A least common multiple of and is a common multiple that is minimal, in the sense that for any other common multiple of and , divides .
let anD be eLemEnTs oF a cOMmutaTIvE rinG . a comMOn mULtIple OF ANd is An eLeMenT oF suCh that bOTh and divide (thAt is, ThERE exist elEmEntS and OF such THat aNd ). a LeAsT commoN mulTipLe of And Is A coMmon multipLe tHaT Is mInIMAl, in thE sense thAt fOR AnY otheR cOmMoN muLTiple OF aND , divides .