最小公倍数是数论中的一个概念。若有一个数X，可以被另外两个数A、B整除，且X大于（或等于）A和B，则X为A和B的公倍数。A和B的公倍数可以有很多个，而所有的公倍数中，最小的公倍数就叫做最小公倍数。两个整数公有的倍数称为它们的公倍数，其中最小的一个正整数称为它们两个的最小公倍数。同样地，若干个整数公有的倍数中最小的正整数称为它们的最小公倍数。n整数的最小公倍数一般记作：，或者参照英文记法记作，其中lcm是英语中“最小公倍数”一词（lowest common multiple）的首字母缩写。

例如，十天干和十二地支的混合称为一个阴历年，干支循环回归同一名称的所需时间，就是12和10的最小公倍数，即是60──一个「甲子」。

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.