Originally Posted by

**Pigzorkly** Hey all, got a homework problem which I'm not quite sure how to go about:

Basically, it wants me to show that an integer M >= 0 is the lcm of the numbers a1, a2, ... an, if and only if it is 1) a common multiple of them all, and 2) if it divides every other common multiple.

It seems easy to prove that **if it divides all common multiples and is a common multiple itself, then it is the lcm (since that's the definition of lcm)**, but the other way around seems a bit trickier - or maybe I'm just getting hung up on some little thing... any idea how to get through this?