GCD and LCM Calculator

Developed by Hemant Parashar, B.Sc.

Find the Greatest Common Divisor (GCD/GCF) and Least Common Multiple (LCM) of two or more numbers with step-by-step factorization steps.

General Purpose Disclaimer

This tool is developed for educational and quick reference purposes. Calculations should be verified independently for critical applications.

Enter Integers

Enter positive integers (comma or space separated):

Understanding GCD and LCM

The **Greatest Common Divisor (GCD)**, also known as the Greatest Common Factor (GCF), of two or more non-zero integers is the largest positive integer that divides all of the numbers without a remainder.

The **Least Common Multiple (LCM)** of two or more non-zero integers is the smallest positive integer that is divisible by all of the numbers.

Method of Prime Factorization

One of the most robust ways to calculate both GCD and LCM is to write the prime factorization of each number:

**GCD:** Find the common prime factors and multiply them using the lowest exponent present in any of the factorizations.
**LCM:** Take all prime factors present in any of the factorizations and multiply them using the highest exponent present.

Example Calculation

For numbers 24 and 36:

            24 = 2³ × 3¹

            36 = 2² × 3²

            GCD = 2² × 3¹ = 4 × 3 = 12

            LCM = 2³ × 3² = 8 × 9 = 72

This tool was developed and verified by Hemant Parashar, B.Sc. Graduate, to provide educational math resources.