Category:Definitions/Lowest Common Multiple
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This category contains definitions related to Lowest Common Multiple.
Related results can be found in Category: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 $b$ 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 $m$.
Integers
For all $a, b \in \Z: a b \ne 0$, there exists a smallest $m \in \Z: m > 0$ such that $a \divides m$ and $b \divides m$.
This $m$ is called the lowest common multiple of $a$ and $b$, and denoted $\lcm \set {a, b}$.
Pages in category "Definitions/Lowest Common Multiple"
The following 9 pages are in this category, out of 9 total.
L
- Definition:Least Common Multiple
- Definition:Lowest Common Multiple
- Definition:Lowest Common Multiple/Also known as
- Definition:Lowest Common Multiple/Integers
- Definition:Lowest Common Multiple/Integers/Definition 1
- Definition:Lowest Common Multiple/Integers/Definition 2
- Definition:Lowest Common Multiple/Integers/General Definition
- Definition:Lowest Common Multiple/Integers/Warning
- Definition:Lowest Common Multiple/Integral Domain