Smallest positive number divisible by two integers
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, lowest common multiple, or smallest common multiple 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.[1][2] Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.[3] However, some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0.
The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions.
The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm(a, b, c, . . .), is defined as the smallest positive integer that is divisible by each of a, b, c, . . .[1]
^ abWeisstein, Eric W. "Least Common Multiple". mathworld.wolfram.com. Retrieved 2020-08-30.
^Hardy & Wright, § 5.1, p. 48
^Long (1972, p. 39)
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