GCD and LCM (Free)
Find the greatest common divisor and least common multiple of two integers.
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Multi-Number GCD & LCM
Calculate GCD and LCM for three or more numbers, with full prime factorization trees and step-by-step proofs.
Frequently Asked Questions
What is the greatest common divisor (GCD)?
The GCD of two integers is the largest positive integer that divides both without a remainder. For example, GCD(48, 18) = 6.
What is the least common multiple (LCM)?
The LCM is the smallest positive integer divisible by both numbers. LCM(4, 6) = 12. It is useful for adding fractions with different denominators.
How does the Euclidean algorithm find the GCD?
The Euclidean algorithm repeatedly divides the larger number by the smaller and takes the remainder, until the remainder is zero. The last non-zero remainder is the GCD.