Least Common Multiple ( LCM )

What do you mean by Least Common Multiple ( LCM ) ? 

Least Common Multiple is the smallest number which is the multiple of two or more numbers. 

For Example

The Least common multiple of 8 and 12 is 24

It means 24 is the lowest number which is the common multiple of 8 and 12.

Least Common Multiple is also called as Lowest Common Multiple.

It is denoted as LCM shortly.

Before finding the LCM of numbers we should have a concrete idea about the Multiples and  Common Multiples.

What are Common Multiples ?

Common multiples are the numbers which are the multiples of two or more numbers in common.

For example

The common multiples of 2 and 4 are 4 , 8 , 12 , 16 , 20 , 24 etc.

How to find out the Common Multiples ?

The common multiples of two or more numbers can be calculated in the following way.

Let's find out the common multiples of 8 and 12

First find out the multiples of 8 then find out the multiples of 12

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

Multiples of 12 are 12 , 24 , 36 , 48 , 60 , 72 , 84 , 96 , 108 , 120 ...

The multiples which are the multiples of both the numbers 8 and 12 are :

24 , 48 , 72 ....

Hence the common multiples of 8 and 12 are 24 , 48 , 72 , 96 etc.

How to find the LCM ?

For finding the LCM of two or more numbers, we have to calculate the multiples of all the given numbers. Then calculate the common multiples. After that we can find out the lowest multiple which is common for all the given numbers. This multiple will be the LCM of the given numbers.

For example

Find the LCM of 4 , 6 and 8

Solution :

The multiples of 4 are 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 , 40 , 44 , 48 , 52 , 56 , 60 ...

The multiples of 6 are 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 , 60 , 66 , 72 , 78 , 84 , 90 .....

The multiples of 8 are 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80 , 88 , 96 , 104 , 112 , 120 ....

4 , 6 and 8 have number of multiples as common. They are 

24 , 48 , 72 , ...

The lowest common multiple ( LCM ) of 4 , 6 , 8 is 24

Did you know ?

Exercise

1. Find the LCM of the following numbers

• 8 , 12 and 16
• 5 , 11 and 13
• 5 , 15 , 20

2. Find the LCM of the following numbers.

• 5 and 6
• 22 and 23
• 58 and 59
• 3 and 5
• 17 and 19

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Multiples

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Multiples

 What are Multiples ?

We know the numbers 1 , 2 , 3 , 4 , 5 ....... When these numbers are multiplied with the same number or another number , then we get the product of the numbers. This product of the numbers is the multiple of the numbers multiplied.

Example 1

Example 2

How can we find the multiples of a number ?

Finding multiples of any number seems very easy. We can follow the procedure mentioned below.

Example 1

Find out any five multiples of the number 15.

Any five multiples of 15 are as follows :

15 X 1 = 15      15 X 2 = 30     15 X 3 = 45      15 X 4 = 60     15 X 5 = 75

Hence, the five multiples of 15 are 15 , 30 , 45 , 60  and 75

Example 2

Find out any five multiples of 24.

Any five multiples of 24 are as follows :

24 X 1 = 24      24 X 5 = 120     24 X 8 = 192      24 X 10 = 240     24 X 15 = 360

Hence, the five multiples of 24 are 24 , 120 , 192 , 240  and 360

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Properties of Multiples

• We get multiple of a number by multiplying the given number with another number or the same number
• The lowest multiple of a number is the number itself.
• We can calculate infinite number of multiples.
• Any number is the multiple of itself. For example, 3 is the multiple of 3.
• All the numbers are the multiples of 1.

Exercise

Find any five multiples of the given numbers

12 , 25 , 48 , 26 , 6

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Least common Multiples ( LCM )