LCM & GCD Calculator
Calculate LCM and GCD with step-by-step Euclidean algorithm.
6
GCD (Greatest Common Divisor)
144
LCM (Least Common Multiple)
2^4 Γ 3
Prime Factors of 48
2 Γ 3^2
Prime Factors of 18
Euclidean Algorithm Steps (GCD)
48 = 18 Γ 2 + 1218 = 12 Γ 1 + 612 = 6 Γ 2 + 0β΄ GCD(48, 18) = 6About This Tool
The GCD (Greatest Common Divisor) is the largest integer that divides both numbers without a remainder. The LCM (Least Common Multiple) is the smallest positive integer divisible by both numbers. They are related by: LCM(a, b) = |a Γ b| / GCD(a, b).
Use Cases
Simplifying fractions (divide by GCD), finding a common denominator (use LCM), scheduling problems where two events repeat on different cycles (LCM = next coincidence), and number theory proofs.