How To Find LCM?

LCM stands for Least Common Multiple. It is the smallest common multiple of a group of numbers. Multiple is a numerical result of the multiplication between the integer and a name. To find the least common multiple (from here on I will address it as LCM) of a group of numbers (maybe 2 or more than 2), you have to know about the factors of the numbers first.

To find LCM, there are various ways. Here, we will discuss some of them. Let’s start with a simple one.

Finding LCM by Listing Multiples:

It is a simple method, and it’s capacity ranges from seeing the LCM value for 2 to 10 numbers. If you are calculating for more significant digits, then you should consider using any other methods.

Let’s say we have to find the LCM of two numbers, i.e. 5 & 8. First, write down all the multiples of each number. Multiples are the result of the multiplication between a number and an integer. Naturally, you can find the multiples on a multiplication table.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

In both cases, we have written the multiples up to 10th standard. Now, find the smallest common numerical value for both the numbers. Here, the lowest common value for 5 & 8 is 40. So, the LCM of 5 & 8 is 40.

Finding LCM by Prime Factorization:

This is another method to find the LCM of a group of numbers. It differs from the simple way mentioned above. Using this method you can see the LCM of the numbers those are more significant than 10.

Let’s say; we have two numbers. Those are 20 & 84. Both of the numbers are greater than 10. If you have a smaller number than 10, then you can use the above method to find the LCM.

Now factorise the numbers you have with their prime factors. Start by writing the natural elements of the numbers. After that, try factorising all the up to you reach only prime numbers.

For 20, we can write, 20 = 2 X 10

Further, we can factorize 10. Now 10 = 2 X 5

Now write all the factors together. Then we have,

20 = 2 X 2 X 5 –    –    –    –    –    –    –    –    –    –    (1)

In the same way, Now factorize the second number, 84.

84 = 42 X2

42 = 6 X 7

6 = 2 X 3

Now after writing all the factors together, we have,

84 = 2 X 3 X 7 X 2 –    –    –    –    –    –    –    –    –    (2)

Compare the equation (1) and equation (2), take common the factors with the same values and write the RHS of the two equations together.

In equation (1) & (2), we have two as a common factor. After taking common from both the equation, we can rewrite the factors as

2 X 2 X 3 X 5 X 7 = 420

Hence, the multiplication of the factors is the least common Multiple of the two number, i.e. 420.

Here, we have discussed the least common Multiple and how to find that. I’ve also illustrated two methods to find the values for different conditions. You can take more examples for your practical purposes.