GCD & LCM Calculator Find the Greatest Common Divisor and Least Common Multiple of two or more numbers.

The GCD is computed using the Euclidean algorithm: GCD(a, b) = GCD(b, a mod b), repeating until the remainder is 0, at which point the other number is the GCD. This runs in O(log(min(a,b))) time. For multiple numbers, GCD is associative: GCD(a,b,c) = GCD(GCD(a,b), c). The LCM for two numbers is computed as LCM(a,b) = |a×b| / GCD(a,b), which avoids the less efficient method of listing multiples. For multiple numbers, LCM is also associative: LCM(a,b,c) = LCM(LCM(a,b), c). The identity GCD(a,b) × LCM(a,b) = |a×b| only holds for exactly two numbers. The calculator takes absolute values of all inputs since GCD and LCM are defined for positive integers. Numbers equal to zero are excluded since every integer divides zero, making GCD trivially equal to the other number, and LCM involving zero is zero.