GCF and LCM Calculator
Find the greatest common factor and least common multiple of two whole numbers.
How it works
GCF by Euclid’s algorithm · LCM = a × b ÷ GCF
The GCF (also called GCD or HCF) is the largest number dividing both inputs; Euclid’s algorithm finds it by repeatedly replacing the larger number with the remainder of the division. The LCM is the smallest number both divide into, and the two are linked: GCF × LCM always equals the product of the original numbers.
Worked example
For 24 and 36: 36 ÷ 24 leaves remainder 12, and 24 ÷ 12 leaves remainder 0, so GCF = 12. Then LCM = 24 × 36 ÷ 12 = 72. Check: 12 × 72 = 864 = 24 × 36.
Frequently asked questions
What are GCF and LCM actually used for?
GCF simplifies fractions and splits things into equal groups; LCM finds common denominators and answers "when do two repeating events line up again" — two buses every 24 and 36 minutes meet every 72.
What if the two numbers share no factors?
Then they are coprime: the GCF is 1 and the LCM is simply their product. For example, 8 and 15 give GCF 1 and LCM 120.
Can I do more than two numbers?
Yes, fold the results in: GCF(a, b, c) = GCF(GCF(a, b), c), and the same chaining works for LCM. Run this calculator twice, feeding the first answer back in.
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This calculator is for educational purposes. Double-check important results before acting on them.