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LCM and GCD Calculations

In this section, let us understand how to calculate the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of numbers.

Before beginning the discussion, we need to learn what are the factors and multiples of a number.


Factors of a number are the numbers which will divide the given number without leaving any remainder.

For example, the factors of 20 are 1,2,4,5,10 and 20


Multiples of a number are generated by multiplying other integers with the given number.

For example, the multiples of 6 are 6,12,18,24,30…

Greatest Common Divisor (GCD)

The greatest common divisor of two numbers is the largest number that will divide both numbers without leaving a reminder. It is also called as Highest Common Factor (HCF).

Consider the numbers 12 and 15.
Factors of 12 are 1,2,3,4,6,12
Factors of 15 are 1,3,5,15
Common Factor are 1, 3
Highest common factor is 3.
So, 3 is the Greatest Common Divisor of 12 and 15.

Least Common Multiple (LCM)

The Least Common Multiple of two numbers is the lowest number that is the multiple of both the numbers

Example Consider the number 10 and 15. Multiples of 10 are 10,20,30,40,50,60,70,80,90,100… Multiples of 15 are 15,30,45,60,75,90,105,120,135… Here the common multiples of 10 and 15 are 30,60,90… Therefore, the Least Common Multiple is 30 Note: The same concepts of GCD and LCM can be extended for more than two numbers.

Finding HCF and LCM using Prime Factorization Method

Let’s take two number 30 and 50 for which we want to find the LCM and GCD.

Step 1: Write each number as the product of its prime factors

30 = 2 x 3 x 5
50 = 2 x 5 x 5

Step 2: This is an optional step. To make further calculations easier, write these factors in a way such that each new factor begins in the same place

30 = 2 x 3 x 5
50 = 2 x 5 x 5

This step allows us to match up the factors.

Facts about GCD and LCM

How to use CalculatorHut’s LCM and GCD calculator?

Enter the numbers separated by commas in the box and click Calculate to find out the GCD and LCM of the number. Our LCM and GCD calculator is very useful in finding out LCM and GCD for larger values and many numbers, where it is very difficult to find out manually.

You can also conveniently add our LCM and GCD calculator widget to your website and make calculations instantly. Just let us know your preferred customizations at [email protected], and we would design an attractive and colorful widget as per your taste. And all this is for FREE!!

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