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least common multiple

Also known as L.C.M, LCM, lowest common multiple, smallest common multiple

smallest positive integer divisible by two or more integers

AI overview

The least common multiple is the smallest positive whole number that can be divided evenly by two or more given numbers. It matters because it helps solve practical problems involving repeating cycles or schedules, such as finding when events that occur at different intervals will happen at the same time.

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Image: Symmetrical 5-set Venn diagram LCM 2 3 4 5 7.svg

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Commons category: Least common multiple

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A Venn diagram showing the least common multiples of all subsets of {2, 3, 4, 5, 7}

In arithmetic and number theory, the least common multiple (LCM), lowest common multiple, or smallest common multiple (SCM) of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0.