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LCM Calculator

Find the least common multiple of two numbers — computed through the GCF identity, with the shared multiples listed.

Written by Jude Ramsey · Last updated August 2026 · How these calculators are checked

How the LCM is found

The least common multiple is the smallest number both inputs divide into — the number you need when adding fractions with different denominators or synchronising repeating cycles. Listing multiples until they collide works but scales terribly; this calculator uses the clean identity LCM = a × b ÷ GCF, shows that working, and lists the first shared multiples as a sanity check.

How to use it

  1. Enter the two whole numbers.
  2. Read the LCM and the GCF-based working.
  3. Check the first few common multiples underneath.

The identity

lcm(a, b) = a × b ÷ gcf(a, b)

A worked example

For 12 and 18 the GCF is 6, so the LCM is 12 × 18 ÷ 6 = 36 — confirmed by the shared multiples 36, 72, 108. The everyday payoff: to add 1/12 + 1/18, the common denominator is exactly that 36, giving 3/36 + 2/36 = 5/36. Cycles work the same way — events every 12 and every 18 days coincide every 36.

Common questions

Why is the LCM never smaller than the larger number?
The LCM must be a multiple of both inputs, and the smallest multiple of the larger number is itself — so the LCM starts there and can only go up.
What if one number divides the other?
Then the larger number is the LCM: lcm(6, 18) = 18, because 18 is already a multiple of 6.
How does this work for three or more numbers?
Fold it: lcm(a, b, c) = lcm(lcm(a, b), c). Run the calculator twice, feeding the first result into the second.

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