GCD & LCM Calculator
Free GCD and LCM calculator. Calculate the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers with a step-by-step breakdown using the Euclidean algorithm.
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What Are the GCD and LCM?
The Greatest Common Divisor (GCD) is the largest number that divides two or more numbers exactly. The Least Common Multiple (LCM) is the smallest number that is a multiple of all the given numbers. Both concepts are fundamental in arithmetic and algebra.
Euclidean Algorithm
The GCD is efficiently computed using the Euclidean algorithm: divide the larger number by the smaller one and repeat with the remainder until it reaches zero. The LCM is derived from the relationship: LCM(a, b) = (a × b) / GCD(a, b).
Frequently Asked Questions
What is the GCD used for?
The GCD is used to simplify fractions, find common denominators, and solve divisibility problems.
What is the LCM used for?
The LCM is used to add fractions with different denominators and to solve problems involving cycles and periodicity.