Art of Problem Solving

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*[[Common multiple]]
*[[Common multiple]]
*[[Least common multiple]]
*[[Least common multiple]]
[[Category:Number Theory]]

Revision as of 15:44, 17 April 2008

A multiple of a given integer is the product of that integer with some other integer. Thus $k$ is a multiple of $m$ exactly when $k$ can be written in the form $nm$ where $n$ and $m$ are integers. (In this case, $k$ is a multiple of $n$, as well). Every integer has an infinite number of multiples. As an example, a few of the multiples of 15 are 15, 30, 45, 60, and 75. A few of the multiples of 3 are 3, 6, 9, 12, and 15.

An equivalent phrasing is that $k$ is a multiple of $m$ exactly when $k$ is divisble by $m$.


See also