GCD & LCM Calculator
Compute the GCD (HCF) and LCM of any set of whole numbers.
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Formula
About this calculator
The greatest common divisor (GCD), also called the highest common factor (HCF), is the largest integer that divides every number in a set without a remainder. The least common multiple (LCM) is the smallest positive integer that every number divides into evenly.
This tool computes the GCD with the Euclidean algorithm and the LCM using the identity LCM(a, b) = |a·b| / GCD(a, b), folding the operation across the whole list. GCD and LCM are essential for simplifying fractions, finding common denominators, and solving scheduling problems.
Frequently asked questions
It repeatedly replaces the larger number with the remainder of dividing the two numbers until one becomes zero; the other is the GCD. It is fast and works for arbitrarily large integers.
Yes. Greatest common divisor (GCD) and highest common factor (HCF) are two names for the same value.
The product of two numbers equals the product of their GCD and LCM, so dividing the product by the GCD gives the LCM directly.
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