Least Common Multiple

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Formal Definition

Let $r_1, r_2, ... , r_n$ be positive integers. Their least common multiple (abbreviated lcm) is the positive generator of the cyclic group of all common multiples of the $r_i$, that is, the cyclic group of all integers divisible by each $r_i$ for $i=1,2,...,n$.

Informal Definition

The least common multiple of a group of numbers is the smallest positive number that is divisible by those numbers.


The lcm of 3,15, and 12 is $3*5*4=60$.


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