Definition:Lowest Common Multiple/Integral Domain
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Definition
Let $D$ be an integral domain and let $a, b \in D$ be nonzero.
$l$ is the lowest common multiple of $a$ and $b$ if and only if:
- $(1): \quad$ both $a$ and $b$ divide $l$
- $(2): \quad$ if $m$ is another element such that $a$ and $b$ divide $m$, then $l$ divides $m$.
Also known as
The lowest common multiple is also known as the least common multiple.
It is usually abbreviated LCM, lcm or l.c.m.
The notation $\lcm \set {a, b}$ can be found written as $\sqbrk {a, b}$.
This usage is not recommended as it can cause confusion.
Also see
- Results about Lowest Common Multiple can be found here.