Difference between revisions of "Common multiple"
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| − | The '''common multiple''' of two or more [[positive integer]]s is a [[multiple]] common to those numbers. | + | The '''common multiple''' of two or more [[positive integer]]s is a [[multiple]] common to those numbers. Any [[finite]] [[set]] of positive integers have an [[infinite]] number of common multiples. |
| − | Every common multiple of a | + | Every common multiple of a set of integers is a multiple of the [[least common multiple]] of those integers. |
| + | |||
| + | For example, the least common multiple of 6, 10 and 15 is 30, and the common multiples of 6, 10 and 15 are exactly equal to the multiples of 30. (As a result of [[poset]] theory, this says that in the poset of positive integers ordered by the [[divisor]] [[relation]], [[least upper bound]]s exist for any finite set.) | ||
== See Also == | == See Also == | ||
| − | *[[ | + | * [[Common divisor]] |
| − | + | ||
| + | [[Category:Definition]] | ||
Latest revision as of 11:15, 19 April 2008
The common multiple of two or more positive integers is a multiple common to those numbers. Any finite set of positive integers have an infinite number of common multiples.
Every common multiple of a set of integers is a multiple of the least common multiple of those integers.
For example, the least common multiple of 6, 10 and 15 is 30, and the common multiples of 6, 10 and 15 are exactly equal to the multiples of 30. (As a result of poset theory, this says that in the poset of positive integers ordered by the divisor relation, least upper bounds exist for any finite set.)
