Free GCD and LCM calculator using the Euclidean algorithm. Find the greatest common divisor and least common multiple with steps.
You might also find these calculators useful
Finding the Greatest Common Divisor (GCD) or Least Common Multiple (LCM) of two numbers is essential for simplifying fractions, solving equations, and many practical applications. Our calculator finds both values instantly using the efficient Euclidean algorithm.
The GCD is the largest number that divides evenly into two or more numbers. The LCM is the smallest number that is a multiple of two or more numbers. These concepts are fundamental in number theory, fractions, and solving real-world problems involving cycles and intervals.
Key Relationship
LCM(a,b) × GCD(a,b) = a × bGet both GCD and LCM in a single operation.
Calculate GCD and LCM for two or more numbers simultaneously.
See the step-by-step calculation process.
Use GCD to reduce fractions to their lowest terms.
Use LCM to find the common denominator when adding fractions.
Find when cyclical events will coincide.
Divide items into equal groups of the largest possible size.
GCD is used to simplify fractions to their lowest terms, find common denominators, and solve problems involving equal distribution or grouping.