GCD & LCM Calculator

Calculate the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers.

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Greatest Common Divisor (GCD)

The GCD (also known as the Greatest Common Factor or GCF) is the largest positive integer that divides each of the numbers without a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.

The GCD is useful for simplifying fractions, finding equivalent ratios, and solving problems involving divisibility.

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Least Common Multiple (LCM)

The LCM is the smallest positive integer that is divisible by each of the numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.

The LCM is useful for adding and subtracting fractions with different denominators, finding common time intervals, and solving scheduling problems.

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Relationship Between GCD and LCM

For any two positive integers a and b, there's a useful relationship: GCD(a, b) × LCM(a, b) = a × b

This relationship can be used to calculate one value when you know the other.

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