The GCD is the greatest positive integer that divides every given positive integer without a remainder.

How is GCD calculated?

Use the Euclidean algorithm, repeatedly dividing and replacing the pair with divisor and remainder until the remainder is zero.

How is LCM calculated?

For two positive integers, divide their product by their GCD.

Multiply the minimum exponents of prime factors shared by every number.

Multiply the maximum exponents of all prime factors that appear in any number.

Yes. Continue pairwise with each intermediate result; this calculator supports up to ten numbers.

For two positive integers, GCD(a,b) × LCM(a,b) = a × b.

Tools/🧮 Calculators/GCD & LCM Calculator

Calculate the GCD and LCM of 2–10 numbers with Euclidean steps and prime factorizations.

Version 1.0 · Last Updated: August 11, 2026 · Maintained by ToolLarder

Find the greatest common divisor and least common multiple of 2–10 positive integers with exact arithmetic, Euclidean steps, and prime factors.

The GCD is the greatest positive integer that divides every given number without a remainder.

GCD(a,b) = GCD(b, a mod b)

The LCM is the smallest positive integer divisible by every given number.

LCM(a,b) = |a×b| / GCD(a,b)

Divide the larger number by the smaller and continue with divisor and remainder until the remainder is zero.

a = b×q + r

Use minimum shared exponents for GCD and maximum exponents across all factors for LCM.

GCD: min exponents · LCM: max exponents

Continue sequentially with pairwise results to support up to ten numbers.

GCD(a,b,c)=GCD(GCD(a,b),c)

Test primality, find prime factors, list primes in a range, and calculate neighboring prime numbers.