GCD / LCM Calculator

How to Use the GCD & LCM Calculator

This free online calculator finds the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of any two integers instantly. Follow these simple steps:

1. Enter two numbers — type any whole numbers into the "First Number" and "Second Number" fields. Negative numbers and zero are accepted.
2. Click Calculate — or press Enter. The GCD and LCM appear immediately.
3. Review the steps — the tool displays every step of the Euclidean algorithm so you can follow the division process that leads to the GCD.
4. See the LCM formula — the calculator shows how LCM is derived from GCD using the relationship LCM(a, b) = |a × b| / GCD(a, b).

All calculations run entirely in your browser. No data is sent to any server, and no sign-up is required.

What Is the GCD?

The Greatest Common Divisor (also called the Highest Common Factor) is the largest positive integer that divides both numbers without a remainder. For example, GCD(48, 18) = 6 because 6 is the biggest number that divides both 48 and 18 evenly.

What Is the LCM?

The Least Common Multiple is the smallest positive integer that is divisible by both numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number that both 4 and 6 divide into evenly.

The Euclidean Algorithm

This tool uses the Euclidean algorithm, one of the oldest known algorithms, to compute the GCD. It works by repeatedly dividing the larger number by the smaller and replacing the larger with the remainder until the remainder is zero. The last non-zero remainder is the GCD.