GCD & LCM Calculator

Mathematics frequently involves identifying connections between numbers, with GCD (Greatest Common Divisor) and LCM (Least Common Multiple) being two of the most valuable concepts. Whether you are a student or an educator, understanding these terms helps simplify fractions, solve equations, and address practical issues related to ratios and proportions.

What is GCD (Greatest Common Divisor)?

The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF), is the largest positive integer that divides two or more numbers without leaving a remainder.

In simpler terms, it’s the biggest number that fits perfectly into all the given numbers.

What is LCM (Lowest Common Multiple)?

The Lowest Common Multiple (LCM) is the smallest number that is a multiple of two or more given numbers.

In other words, it’s the smallest positive number that can be divided evenly by all the given numbers.

GCD and LCM Formula

There’s a strong mathematical relationship between GCD and LCM. For any two positive integers 

$$\mathrm{GCD}(a,b)\times \mathrm{LCM}(a,b)=a\times b$$

Example of GCD and LCM Together

Let’s find the GCD and LCM of 15 and 25.

Factors of 15 = 1, 3, 5, 15

Factors of 25 = 1, 5, 25

GCD = 5

Using the formula:

$$\mathrm{LCM}(15,25)=\frac{(15\times 25)}{5}=75$$

LCM = 75

How to find GCD and LCM with our Calculator

1. Enter the data values separated by a comma, space, or a new line. 
2. Choose which value you wish to determine, i.e., GCD, LCM, or Both..
3. The tool automatically finds GCD and LCM.