\begin{definition}[Definition:Lowest Common Multiple/Integral Domain]
Let $D$ be an integral domain and let $a, b \in D$ be nonzero.
$l$ is the '''lowest common multiple''' of $a$ and $b$ {{iff}}:
:$(1): \quad$ both $a$ and $b$ divide $l$
:$(2): \quad$ if $m$ is another element such that $a$ and $b$ divide $m$, then $l$ divides $m$.
\end{definition}