Instantly calculate the greatest common divisor (GCD) and least common multiple (LCM) of any number of integers.
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Separate the numbers with a space or comma. GCD = greatest common divisor; LCM = least common multiple.
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The GCD is the largest number dividing all values exactly, and the LCM is the smallest number divisible by all of them. Both follow from prime factorization or Euclid’s algorithm:
For 12 and 18: GCD = 6, LCM = 36. Check: (12 × 18) ÷ 6 = 216 ÷ 6 = 36.
It is the largest number that divides all the given numbers exactly. The GCD of 12 and 18 is 6.
It is the smallest number that is divisible by all the given numbers. The LCM of 12 and 18 is 36.
Repeatedly divide the larger number by the smaller and replace it with the remainder, until the remainder is 0. The last non-zero divisor is the GCD.
For two numbers: LCM = (a × b) ÷ GCD. For example, (12 × 18) ÷ 6 = 36.
GCD for simplifying fractions; LCM for finding a common denominator and for problems with events that repeat at different intervals.
It is 1. Two numbers are coprime if they share no common divisor other than 1, for example 8 and 15.
Yes. Enter any number of values; the calculator applies the operation successively, two at a time.
GCD = 6 (greatest common divisor), and LCM = 72 (least common multiple of the three).
Yes. The greatest common divisor (GCD) is also called the highest common factor (HCF) or greatest common factor (GCF) — all three name the same value: the largest whole number that divides every input exactly.