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GCD & LCM Calculator

Find the greatest common divisor and least common multiple of two or more numbers with step-by-step prime factorization.

Enter at least two valid positive integers.

Greatest Common Divisor

—

Coprime

Least Common Multiple

—

Relationship Verification

GCD(0, 0) × LCM(0, 0) = 0

|0 × 0| = 0

Verified: GCD × LCM = |a × b|

Prime Factorizations

How to use

  1. 1

    Enter your numbers

    Type two or more positive integers into the input fields. Click '+' to add more fields (up to 10).

  2. 2

    View results

    The GCD and LCM are calculated instantly and displayed prominently.

  3. 3

    See the working

    Click 'Show steps' to see the prime factorization method and Euclidean algorithm used to find the answer.

Frequently asked questions

What is the difference between GCD and LCM?
The GCD (greatest common divisor) is the largest number that divides all given numbers evenly. The LCM (least common multiple) is the smallest number that all given numbers divide into evenly.
What is the Euclidean algorithm?
A method for finding the GCD of two numbers: repeatedly replace the larger number with the remainder of dividing the larger by the smaller, until the remainder is zero.
How are GCD and LCM related?
For two numbers a and b: GCD(a,b) x LCM(a,b) = |a x b|. This is verified live in the calculator.
What does coprime mean?
Two numbers are coprime when their GCD equals 1, meaning they share no common factor other than 1.

Calculate the GCD (greatest common divisor) and LCM (least common

multiple) of up to ten numbers simultaneously. See the solution worked

out step by step using both the prime factorization method and the

Euclidean algorithm. The relationship GCD x LCM = |a x b| is verified

live. All processing runs entirely in your browser.

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