GCD & LCM Calculator

Find the greatest common divisor and least common multiple of two or more numbers, with Euclid’s steps.

How do you find the GCD and LCM?

The GCD is the largest number that divides all the numbers; Euclid’s algorithm finds it by repeated division with remainder. The LCM is the smallest number they all divide into: LCM(a, b) = a × b ÷ GCD(a, b). For 12, 18 and 30 the GCD is 6 and the LCM is 180.

Where it is used

GCD: simplifying fractions (18/30 ÷ 6 = 3/5), splitting things into equal groups.
LCM: common denominators, repeating schedules (buses every 12 and 18 minutes meet every 36).

Frequently asked questions

Is GCD the same as HCF?

Yes — greatest common divisor, greatest common factor and highest common factor are the same thing.

What does co-prime mean?

Numbers whose GCD is 1, like 8 and 15.

How large can the numbers be?

Any size — it uses exact big-integer arithmetic.