Page 190 - New Medley 4 Semester 1

Example 8: Find the HCF of 36 and 30.

Solution: Factors of 36: 1 , 2 , 3 , 4, 6 , 9, 12, 18, 36

Factors of 30: 1 , 2 , 3 , 5, 6 , 10, 15, 30

Here, common factors of 36 and 30 are 1, 2, 3 and 6.
The greatest common factor among 1, 2, 3 and 6 is 6, so,

6 is the HCF of 36 and 30.

Least Common Multiple (LCM): The smallest number which is divisible by
all the given numbers is called the least common multiple.

Here, we will find the LCM of the given numbers using the common multiple

method.

Example 9: Find the LCM of 6 and 4.

Solution: Multiples of 6: 6, 12 , 18, 24 , …

Multiples of 4: 4, 8, 12 , 16, 20, 24 , 28, 32,...

Here, common multiples of 6 and 4 are 12, 24,...
\ LCM of 6 and 4 is 12.

Example 10: Find the LCM and HCF of 12 and 18. Is there any
relationship between the two?

Solution: Multiples of 12: 12, 24, 36 , 48, 60, 72 , …

Multiples of 18: 18, 36 , 54, 72 , 90,...

Here, common multiples of 12 and 18 are 36, 72, …

\ LCM of 12 and 18 is 36.

Again, factors of 12: 1 , 2 , 3 , 6 , 12

and factors of 18: 1 , 2 , 3 , 6 , 9, 18

Here, common factors of 12 and 18 are 1, 2, 3 and 6.
\ HCF of 12 and 18 is 6.

Yes, we find a relationship between LCM and HCF. LCM of two or more
numbers is always divisible by their HCF. Also, we can say that LCM is a
multiple of HCF of the given numbers.

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