Calculators

GCD & LCM

Find the greatest common divisor and least common multiple of two whole numbers. Useful for simplifying fractions, scheduling cycles and number theory.

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💡 Good to know: Euclid's algorithm for the GCD is over 2,000 years old and still among the fastest known — computers run it essentially unchanged.

Worked example

GCD: 12 · LCM: 72

How it’s solved

Worked on the example above, step by step — follow along and you can do it on paper next time, no tool required.

The GCD is the largest number dividing both; Euclid's method keeps replacing the pair with (smaller, remainder) until the remainder hits 0.
Run Euclid's algorithm
36 = 24 × 1 + 12; 24 = 12 × 2 + 0
The last divisor before the 0 remainder is the GCD
GCD = 12
LCM = |a × b| ÷ GCD
|24 × 36| ÷ 12 = 72

Learn the method

Inputs

A
24
B
36

Frequently asked

What are the GCD and LCM of 24 and 36?

GCD 12 and LCM 72.

How is the LCM found?

It's the product of the two numbers divided by their GCD.