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
SYLADA@11
ReplyDelete