How do I find a lowest common multiple quickly?

Divide the product of the two numbers by their greatest common divisor. For 12 and 18 that is 216/6 = 36. Listing multiples until they match works but is slow once the numbers are large.

What is the LCM used for outside exams?

Anything with repeating cycles that have to line up: gear teeth returning to the same position, shift rotas, payment schedules on different frequencies, and finding a common denominator for fractions.

Math & Statisticsnumber theory

LCM Calculator

Lowest common multiple of a list of integers, computed through the GCD rather than by enumerating multiples.

Also called: lowest common multiple calculator, least common multiple.

Lowest common multiple

The LCM is 60 and the GCD is 1.

Greatest common divisor

How this is calculated

Method and background

How this is calculated

The product of two numbers equals their GCD times their LCM, so dividing the product by the GCD gives the LCM directly. Enumerating multiples until one matches is the schoolbook method and is unusably slow on large numbers.

lcm = |a*b| / gcd(a,b)

a, b: The two numbers

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

lcm of 4, 6, 15

Numbers: 4, 6, 15

Lowest common multiple60

independently verified by prime factorisation

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a multiple absorbs its factor

Numbers: 5, 20

Lowest common multiple20

boundary

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an empty list

Numbers

Lowest common multiple0

degenerate case

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Frequently asked questions

How do I find a lowest common multiple quickly?: Divide the product of the two numbers by their greatest common divisor. For 12 and 18 that is 216/6 = 36. Listing multiples until they match works but is slow once the numbers are large.
What is the LCM used for outside exams?: Anything with repeating cycles that have to line up: gear teeth returning to the same position, shift rotas, payment schedules on different frequencies, and finding a common denominator for fractions.