LCM & GCF Calculator

How to Find GCF and LCM

GCF (Greatest Common Factor) is the largest number that divides all your values evenly. LCM (Least Common Multiple) is the smallest number that all your values divide into evenly.

How the GCF is found

  1. The calculator uses the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is 0.
  2. The last non-zero remainder is the GCF.

How the LCM is found

  1. Once you have the GCF, the LCM is calculated as: LCM = (A × B) ÷ GCF
  2. For more than two numbers, the calculator chains the operation pairwise.

Worked example

For 12 and 18: GCF = 6 (the largest number dividing both). LCM = (12 × 18) ÷ 6 = 36 (the smallest number both divide into).

When to use

GCF is used to simplify fractions. LCM is used to find common denominators, schedule repeating events, and solve fraction addition problems.