GCD and LCM Calculator — Find Greatest Common Divisor & Least Common Multiple

Numbers (comma-separated)Enter at least two valid positive integers, separated by commas.

Greatest Common Divisor (GCD)

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Least Common Multiple (LCM)

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How to Use This Tool

Enter two or more positive integers, separated by commas.
Click Calculate for the GCD and LCM.

GCD and LCM Definitions

The Greatest Common Divisor (GCD) is the largest number that divides evenly into all your given numbers. The Least Common Multiple (LCM) is the smallest number that all your given numbers divide evenly into.

The Euclidean Algorithm

This calculator finds GCD using the Euclidean algorithm — repeatedly replacing the larger number with the remainder of dividing it by the smaller number, until the remainder is zero. This is one of the oldest and most efficient algorithms in mathematics.

LCM(a, b) = (a × b) ÷ GCD(a, b)

Common Uses

GCD: Simplifying fractions to lowest terms, dividing items into equal groups
LCM: Finding a common denominator when adding fractions, scheduling repeating events (e.g., "when will these two events next coincide?")

Frequently Asked Questions

How does the Euclidean algorithm find GCD so efficiently?

It repeatedly replaces the larger number with the remainder of dividing it by the smaller number until the remainder reaches zero — this converges very quickly, even for very large numbers, making it one of the most efficient known GCD algorithms.

What is GCD and LCM used for in real life?

GCD is commonly used to simplify fractions to their lowest terms, while LCM is used to find common denominators when adding fractions, or to determine when repeating events (like bus schedules) will next align.

This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.