The GCF (Greatest Common Factor), also called GCD, is the largest number that divides all given numbers. E.g. GCF(12, 18) = 6.

The LCM (Least Common Multiple) is the smallest positive number divisible by all given numbers. E.g. LCM(4, 6) = 12.

How is GCF calculated?

Using Euclid's algorithm: gcd(a, b) = gcd(b, a mod b). E.g. gcd(48, 18): 48=2×18+12, 18=1×12+6, 12=2×6+0. GCF=6.

What are common uses of LCM?

LCM is used to find common denominators when adding fractions, to synchronize repeating events, and in scheduling problems.

📐 LCM & GCF Calculator

Calculate the Least Common Multiple (LCM) and Greatest Common Factor (GCF) for 2-6 numbers. Enter numbers separated by commas — the calculator also shows the prime factorization.

Numbers (2-6 numbers, comma-separated)

LCM (Least Common Multiple)

GCF (Greatest Common Factor)

Prime factorizations

12=2^2 × 3

18=2 × 3^2

24=2^3 × 3

The LCM and GCF calculator finds the least common multiple and the greatest common factor of two up to six numbers and shows their prime factorization. It is a clear aid for fraction problems, division tasks and any number theory practice.

How the calculator works and what it’s for▾

What LCM and GCF mean

The greatest common factor (GCF) is the largest number that divides all the given values evenly. The least common multiple (LCM) is the smallest number that is a multiple of all of them.

For 12 and 18, the GCF is 6 and the LCM is 36. The two ideas often go hand in hand when adding or reducing fractions.

How the calculation works

The tool breaks each number into its prime factors. The GCF is built from the shared primes at their lowest powers, and the LCM from all primes at their highest powers.

Showing the prime factorization keeps the process transparent, so you can see how the result was reached rather than just a final figure.