 LCM is an exciting concept in Mathematics. The least common multiple of any two numbers is the number that is divisible by both the numbers. LCM is also commonly referred to as LCD. The full form of LCD is Least Common Divisor. The concept of LCM is introduced at an early stage to the students. It is one of the concepts that make Math easier. Also, students have a great time exploring Least Common Multiples.

LCM also has wide applications in Algebra. It is used in the addition or subtraction of any two fractions. When you perform operations such as addition, subtraction with fractions, the denominators need to be the same. This is where LCM is used. LCM makes the process of simplification simple and easy so that we can perform operations on fractions. LCM has many other applications. Cuemath is an online learning platform that helps you understand the concept of LCM in a detailed way with the help of math experts. Cuemath uses modern learning techniques like simulations, math games, puzzles, etc., in order to make learning fun and interesting.

In this blog, we are going to explore various aspects of the Least Common Multiple. We will go through various methods by which you can find the LCM of a number. Let us get started with the blog :

## Defining LCM (Least Common Multiple)

LCM ( Least Common Multiple ) is a method by which we can find the smallest common multiple of two or more numbers. A common multiple is a number that is divisible by two or more numbers that are grouped together in the LCM. We start learning LCM by finding the least common multiple of only two numbers. Gradually, we can group more than two numbers and find their LCM using some simple and engaging methods. Let us explore some of the methods by which we can find the LCM of a number.

## Methods to Find LCM

Now that we know that the Least Common multiple is used to find the smallest common multiple of two or more given numbers, we are now going to explore various ways by which we can find the least common multiples of two or more numbers.

### Listing the Multiples Method

Using this method, we list down the multiples of the given numbers and then find the multiples that are common between these numbers. E.g., 4 and 2 are two numbers. The multiples of 4 are 2 and 2, and the multiples of 2 are 2 and 1. Here the common multiple of 4 and 2 is 2. Hence the LCM (4,2) is 2.

### Prime Factorisation Method

Using this method, we list down the factors of the given numbers. After writing the prime factors of these numbers, we need to find the factors that are common between these numbers. Suppose we take three numbers, 3,6, and 9.

• Prime factors of 3 = 3 × 1
• Prime factors of 6 = 2 × 3
• Prime factors of 9= 3 × 3

Here, the only common factor is 3. Hence the LCM of 3,6 and 9 is 3.

### LCM by Division Method

Using the division method is a bit complex. SO, let us break it into steps:

• Write all the numbers separated by a comma.
• Now, you need to divide these numbers by the smallest prime number.
• If the number is not divisible, proceed further.
• This process continues until we find the result as 1
• The LCM is the product of all the prime numbers used in the division method. 