The Least Common Multiple (LCM) is the smallest positive number that is evenly divisible by all numbers in the set. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.

What is the GCF (or GCD)?

The Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), is the largest number that divides evenly into all numbers in the set. GCF(12, 18) = 6 because 6 is the largest number that divides both 12 and 18.

How are LCM and GCF related?

For two numbers a and b: LCM(a,b) × GCF(a,b) = a × b. This identity is useful for finding one if you know the other.

When do I need the LCM in real life?

LCM is used when adding or subtracting fractions with different denominators — you need the LCM of the denominators as the common denominator. GCF is used to simplify fractions to their lowest terms.

Math

● Math

LCM & GCF calculator

Enter a list of whole numbers — get the least common multiple, greatest common factor, and prime factorization of each.

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GCF / GCD

Greatest common factor

LCM

Least common multiple

Prime factorization

12 = 2 × 2 × 3

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

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