The least common multiple (LCM) of two integers a and b is the smallest positive integer that is a multiple of both a and b. If there is no such positive integer, i.e., if either a or b is zero, then lcm(a,b) is defined to be zero.
The least common multiple is useful when adding or subtracting fractions, because it yields the lowest common denominator. Consider for instance
In case not both a and b are zero, the least common multiple can be computed by using the greatest common divisor (or GCD) of a and b,
a b  
lcm(a, b) =   
gcd(a, b) 
Thus, the Euclidean algorithm for the GCD also gives us a fast algorithm for the LCM. As an example, the LCM of 12 and 15 is 12 × 15 / 3 = 60.
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