Definition:Lowest Common Multiple/Integral Domain

Definition
Let $D$ be an integral domain and let $a, b \in D$ be nonzero.

$l$ is the lowest common multiple of $a$ and $b$ :
 * $(1): \quad$ both $a$ and $b$ divide $l$
 * $(2): \quad$ if $m$ is another element such that $a$ and $b$ divide $m$, then $l$ divides $m$.