What is "least common multiple"

Multiple \Mul"ti*ple\, n. (Math.) A quantity containing another quantity an integral number of times without a remainder.

Note: A

common multiple of two or more numbers contains each of them a number of times exactly; thus, 24 is a common multiple of 3 and 4. The

least common multiple is the smallest number that will do this; thus, 12 is the least common multiple of 3 and 4 (abbreviated LCM).

n. (context mathematics English) The smallest number which may be divided by any of a set of numbers without a remainder.

n. the smallest multiple that is exactly divisible by every member of a set of numbers; "the least common multiple of 12 and 18 is 36" [syn: lowest common multiple, lcm]

In arithmetic and number theory, the least common multiple (also called the 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. 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, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.

The LCM is familiar from grade-school arithmetic as the " lowest common denominator" (LCD) that must be determined before fractions can be added, subtracted or compared. The LCM of more than two integers is also well-defined: it is the smallest positive integer that is divisible by each of them.