Clarification on a proof: ...Prove m=b iff a|b

[mcwang719]

Hi I'm working on a proof I have the solution but don't understand it fully. The problem is:

Let a and b be natural numbers and LCM(a,b)=m. Prove that m=b if and only if a divides b.
Proof: Suppose LCM(a,b)=b. Then by definition of LCM, a divides b. Suppose a divides b. Then b is a common multiple of a and b; so b>or equal to m. On the other had b divdes m, so b < or equal to m. Therefore b=m.

How can a divide b if b is the LCM, that means b<a?

 

[Gene]

Hmmm.
"How can a divide b if b is the LCM, that means b<a?"
Consider a=3, b=6
LCM(3,6) = 6
Where does your b<a come from