Least common multiple
The least common multiple of two integers is the smallest positive integer between all the multiples of both. It is usually written as LCM(a, b). Likewise, the LCM of more than two integers is the smallest positive integer that is divisible by each of them.
Overview[change | change source]
A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and 2 as well.
Relation with the greatest common divisor[change | change source]
It is known that:
where is the greatest common divisor of a and b, This formula is often used to compute the LCD, by first finding the GCD of a and b.