What is the greatest common factor?

The greatest common factor, or GCF, is the largest whole number that divides into all the numbers with no remainder. For 12 and 18 it is 6. It is used to simplify fractions and ratios.

What is the lowest common multiple?

The lowest common multiple, or LCM, is the smallest number that all the numbers divide into. For 4 and 6 it is 12. It is used to add fractions with different denominators.

How are GCF and LCM related?

For two numbers, the GCF times the LCM equals the product of the two numbers. So once you know one, you can find the other. The calculator works out both directly for any list.

GCF and LCM Calculator

Find the greatest common factor and the lowest common multiple of two or more whole numbers. Enter your numbers separated by commas or spaces, and the calculator shows both at once. The GCF helps simplify fractions, and the LCM helps add them.

Greatest common factor0

Lowest common multiple0

How it works

The calculator uses the Euclidean algorithm to find the GCF of the numbers, taking remainders until one divides the other exactly. The LCM is then found from the rule that, for each pair, the GCF times the LCM equals the product, applied across the whole list.

Worked example

For 12, 18, and 24, the greatest common factor is 6, the largest number dividing all three. The lowest common multiple is 72, the smallest number all three divide into.

Related calculators

Fraction Calculator: add and simplify fractions.
Ratio Calculator: simplify ratios.
Square Root Calculator: roots of a number.
Factorial Calculator: n factorial.

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