Help with elementary question involving a partially ordered set. Let N with divisibility be a partially ordered set. 
Show that any 2 element subset of N has a greatest lower bound and a least upper bound.
I seem to keep going in circles, but I have the idea that if we let $m=ab\in N$ then $a\mid m$ and $b\mid m$, but this only guarantees we have an upper bound.
Any help is appreciated.

HINT: You want the least common multiple and its mate, the greatest ... what?
