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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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There are problems on the least common multiple and arithmetic progressions.
All Middle American civilizations used the two first counts, which permitted officials accurately to determine a date within a period defined as the least common multiple of 260 and 365: 18,980 days, or 52 years.
I don't know how to do the least common multiple and the least common denominator.
He could not grasp the least common multiple of the two sides.
The least common denominator for two fractions is the least common multiple of their denominators.
The order of a permutation is the least common multiple of the lengths in the decomposition into disjoint cycles.

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