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Least common multiple. Formula

What is a formula to calculate the least common multiple?

There is a simple formula to find the least common multiple of two numbers.

The formula to calculate the least common multiple (lcm) of the numbers a and b:

lcm(a, b) =
ab ÷ gcd(a, b)

the gcd(a, b) is the greatest common divisor (factor) of the numbers a and b.

Example

Problem. Find the least common multiple of the numbers 12 and 18.

Solution.

The product of the numbers 12 and 18 are

12 * 18 = 216

The greatest common divisor between the numbers 12 and 18 is 6. See Find the greatest common factor of 12 and 18.

The least common multiple (lcm) of the numbers 12 and 18:

lcm(12, 18) =
216 ÷ 6 = 36

The answer:

lcm(12, 18) = 36