LCM AND HCF
LEAST COMMON MULTIPLE
Definition : The least common multiple of two or more numbers is the least natural number that is a multiple of the given numbers.
L.C.M can be determined by three methods:
1) By writing the multiples of the given numbers.
2) By prime factorisation method
3) By division method.
L.C.M by writing the multiples of given numbers
To find the Least Common Multiple (LCM) of two or more numbers, you can follow these steps:
Let's take an example and find the LCM of 4 and 6.
Step 1: List the Multiples
List the multiples of each number until a common multiple is found.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Step 2: Identify the Least Common Multiple
Find the smallest number that is common in both lists. In this case, the LCM is 12.
Step 3: Result
The LCM of 4 and 6 is 12.
If there are more than two numbers, continue listing the multiples until you find a common multiple. Here's an example with three numbers: 4, 6, and 8.
Step 1: List the Multiples
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
Multiples of 8: 8, 16, 24, 32, 40, ...
Step 2: Identify the Least Common Multiple
The smallest number common in all three lists is 24.
Step 3: Result
The LCM of 4, 6, and 8 is 24.
This method can be extended to more than three numbers as well. Keep listing the multiples until you find the smallest common multiple.
Example- I : Find L.C.M of 2 and 3
Sol : Now multiples of '2' are 2, 4, 6, 8, 10, 12, 14, 16, 18 .......
multiples of '3' are 3, 6, 9, 12, 15, 18 .....
common multiples of '2' and '3' are 6, 12, 18....
Here the least common multiple of 2 and 3 is 6