LCM equals Product iff Coprime

Theorem
Let $a, b \in \Z_{>0}$ be strictly positive integers.

Then:
 * $\lcm \set {a, b} = a b$


 * $a$ and $b$ are coprime
 * $a$ and $b$ are coprime

where $\lcm$ denotes the lowest common multiple.

Necessary Condition
Let $a$ and $b$ be coprime.

Then:

Sufficient Condition
Let $\lcm \set {a, b} = a b$.

Then: