Math

GCD & LCM Calculator

Free GCD and LCM calculator using the Euclidean algorithm. Find the greatest common divisor and least common multiple with steps.

Calculate GCD and LCM Instantly

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.

Understanding GCD and LCM

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 × b

Why Use This Calculator?

Dual Calculation

Get both GCD and LCM in a single operation.

Multiple Numbers

Calculate GCD and LCM for two or more numbers simultaneously.

Detailed Steps

See the step-by-step calculation process.

How to Calculate GCD and LCM

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Common Applications

Simplifying Fractions

Use GCD to reduce fractions to their lowest terms.

Common Denominators

Use LCM to find the common denominator when adding fractions.

Cycle Problems

Find when cyclical events will coincide.

Group Division

Divide items into equal groups of the largest possible size.

Frequently Asked Questions

GCD is used to simplify fractions to their lowest terms, find common denominators, and solve problems involving equal distribution or grouping.