GCD and LCM Calculator

The GCD (also called HCF — Highest Common Factor) is the largest number that divides all given numbers evenly. The LCM is the smallest number that all given numbers divide into evenly. For example, GCD(12, 18) = 6 and LCM(12, 18) = 36.

• GCD — simplifying fractions (divide numerator and denominator by GCD), splitting items evenly into groups
• LCM — finding a common denominator for fractions, scheduling repeating events (e.g., two buses with different intervals)

The calculator uses the Euclidean algorithm for GCD — repeatedly replace the larger number with the remainder of dividing the two. LCM is then computed as (a × b) ÷ GCD(a, b). This approach is efficient even for large numbers.