GCD & LCM Calculator

Find the Greatest Common Divisor and Least Common Multiple of two numbers.

GCD

(Greatest Common Divisor)

6

LCM

(Least Common Multiple)

36

GCD(12, 18) = 6 — both numbers are divisible by 6.

LCM(12, 18) = 36 — the smallest number divisible by both.

Verify: GCD × LCM = 12 × 18 → 6 × 36 = 216 ✓

GCD vs LCM

GCD (Greatest Common Divisor)

The largest number that divides both numbers without a remainder. Used to simplify fractions and find common factors.

GCD(12, 18) = 6

LCM (Least Common Multiple)

The smallest number that is a multiple of both numbers. Used to add fractions with different denominators.

LCM(12, 18) = 36

Key Relationship

GCD(a, b) × LCM(a, b) = a × b

This relationship always holds for any two positive integers. Our calculator verifies this for every result.