GCF & LCM Calculator

The GCF & LCM Calculator finds two fundamental quantities for a set of whole numbers: the Greatest Common Factor (also called the greatest common divisor) and the Least Common Multiple. The GCF is the largest number that divides all of your inputs evenly, while the LCM is the smallest number that all of your inputs divide into evenly. Enter two or more integers and the tool returns both values, which are the building blocks for reducing fractions and finding common denominators.

The standard method for the GCF is the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing it by the smaller until the remainder reaches zero; the last nonzero divisor is the GCF. The LCM is then derived from a tidy relationship: for any two numbers, the GCF multiplied by the LCM equals the product of the numbers, so LCM equals the product divided by the GCF. For three or more inputs the tool applies these operations pairwise across the list.

These values appear constantly in everyday math. The GCF is exactly what reduces a fraction to lowest terms, while the LCM gives the least common denominator when you add or subtract fractions — the same step the Fractions Calculator performs internally. The LCM also answers real scheduling puzzles, like when two repeating events next coincide, and the GCF helps split items into the largest equal groups.

A practical tip: if the GCF of two numbers is 1, the numbers are coprime and their LCM is simply their product. Conversely, when one number divides the other, the smaller is the GCF and the larger is the LCM. Prime factorization is an alternative mental method — take the lowest powers of shared primes for the GCF and the highest powers of all primes for the LCM.