🔢 GCD & LCM Calculator

GCD and LCM Explained

The Greatest Common Divisor (GCD) is the largest number that divides both numbers without a remainder. The Least Common Multiple (LCM) is the smallest number that is a multiple of both numbers. These concepts are fundamental in number theory and have practical applications in simplifying fractions, finding common denominators, and solving scheduling problems.

How They're Calculated

• GCD: Uses the Euclidean algorithm — repeatedly divide the larger number by the smaller and take the remainder until the remainder is 0.
• LCM: Uses the relationship LCM(a,b) = |a × b| / GCD(a,b).

Practical Uses

GCD is used to simplify fractions (e.g., 24/36 = 2/3 since GCD is 12). LCM is useful for finding common denominators when adding fractions and for scheduling problems (e.g., two events that repeat at different intervals).