GCD and LCM Finder
Find the greatest common divisor and least common multiple of a set of numbers.
Shared divisors and multiples
The greatest common divisor is the largest number dividing a set evenly, and the least common multiple is the smallest number they all divide into. This finds both for the numbers you enter, the pair of quantities behind much fraction and cycle work.
Enter your numbers to find the GCD and LCM.
The neat relationship between them
For two numbers, there is an elegant fact worth knowing: the GCD and LCM are linked, and their product equals the product of the two original numbers. So once you have one, the other follows. There is also a classic efficient method for the GCD, the ancient Euclidean algorithm, which finds it by repeated division without needing to factor the numbers — a beautifully simple procedure that is thousands of years old and still the standard way. In practice these come up whenever you work with fractions: the GCD to simplify, the LCM to find a common denominator for adding. They also solve real timing puzzles, like when two repeating events next coincide, which is exactly the least common multiple of their cycles.
Questions & answers
Is there a shortcut between GCD and LCM?
For two numbers, their GCD times their LCM equals the product of the numbers, so knowing one gives the other.
How is the GCD found efficiently?
By the Euclidean algorithm, an ancient method of repeated division that finds it without factoring the numbers — still the standard approach.
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