What is the GCF used for?

Simplifying fractions (divide numerator and denominator by their GCF), finding common denominators, and solving problems involving equal groups or sharing.

What is the LCM used for?

Finding the lowest common denominator when adding fractions with different denominators. Also used in scheduling problems (e.g., when two events will next coincide).

What is the relationship between GCF and LCM?

GCF(a, b) × LCM(a, b) = a × b. This means if you know the GCF, you can find the LCM: LCM = (a × b) / GCF.

What if the GCF is 1?

The numbers are called coprime (or relatively prime). Their LCM equals their product. Examples: 8 and 9 are coprime (GCF=1, LCM=72).

GCF & LCM Calculator

Enter two integers to instantly find their GCF (greatest common divisor) and LCM (least common multiple).

The Greatest Common Factor (GCF) is the largest number that divides both integers evenly. The Least Common Multiple (LCM) is the smallest number that both integers divide evenly into. This calculator finds both using the Euclidean algorithm and prime factorization.

Last reviewed: April 2026Report an error

First Number (A)

Second Number (B)

GCF / LCM

GCF = 12 · LCM = 144

GCF(36, 48) = 12. LCM(36, 48) = 144.

GCF (Greatest Common Factor)

LCM (Least Common Multiple)

144

Prime factors of 36

2 × 2 × 3 × 3

Prime factors of 48

2 × 2 × 2 × 2 × 3

The Formula

GCF × LCM = A × B

GCF = Greatest Common Factor (via Euclidean algorithm)
LCM = Least Common Multiple = A × B / GCF

Source: Khan Academy — GCF & LCM ↗

How we verify our formulas →

How to Use This GCF / LCM Calculator

Enter the first integer.
Enter the second integer.
Read the GCF and LCM instantly.
See the prime factorizations of both numbers.

Frequently Asked Questions

: Simplifying fractions (divide numerator and denominator by their GCF), finding common denominators, and solving problems involving equal groups or sharing.
: Finding the lowest common denominator when adding fractions with different denominators. Also used in scheduling problems (e.g., when two events will next coincide).
: GCF(a, b) × LCM(a, b) = a × b. This means if you know the GCF, you can find the LCM: LCM = (a × b) / GCF.
: The numbers are called coprime (or relatively prime). Their LCM equals their product. Examples: 8 and 9 are coprime (GCF=1, LCM=72).

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GCF & LCM Calculator

The Formula

How to Use This GCF / LCM Calculator

Frequently Asked Questions

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