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What is a least common multiple?

What is a least common multiple? Here are some definitions.

Noun
  1. (mathematics) The smallest number which may be divided by any of a set of numbers without a remainder.
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The order of a permutation is the least common multiple of the lengths in the decomposition into disjoint cycles.
I don't know how to do the least common multiple and the least common denominator.
Last night I had a dream in which I proved the non-existence of God by the least common multiple.
There are problems on the least common multiple and arithmetic progressions.
Finding the least common multiple is an important skill for further dealings with fractions.
For the vast constituencies vote merely along the line of the least common multiple of their mob minds.

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