HCF AND LCM OF DECIMALS

Example 1 :

Find the HCF of 0.12 and 0.16. 

Solution : 

In both 0.12 and 0.16, we have equal number of digits after the decimal point. That is 2.  

Multiply both 0.12 and 0.16 by 100 to get rid of the decimal point.

0.12 x 100  =  12

0.16 x 100  =  16

Find the HCF of 12 and 16.

HCF (12, 16)  =  Product of common factors

=  2 x 2

=  4

Divide the HCF 4 by 100.

4/100  =  0.04

So, the highest common factor of 0.12 and 0.16 is

0.04

Example 2 :

Find the LCM of 0.8 and 0.12. 

Solution :

In 0.8 and 0.12, we have more number of digits after the decimal point in 0.12. That is 2.  

Multiply both 0.8 and 0.12 by 100 to get rid of the decimal point.

0.8 x 100  =  80

0.12 x 100  =  12

Find the LCM of 80 and 12.

LCM (80, 12)  =  Product of all prime factors

=  2 x 2 x 2 x 2 x 3 x 5

=  240

Divide the LCM 240 by 100.

240 / 100  =  2.4

So, the least common multiple of 0.8 and 0.12 is

2.4

Example 3 :

Find the HCF of 0.6, 0.75 and 1.05. 

Solution :

In 0.6, 0.75 and 0.105, we have more number of digits after the decimal point in 0.75 and 1.05. That is 2.  

Multiply the given numbers by 1000 to get rid of the decimal point.

0.6 x 100  =  60

0.75 x 100  =  75

1.05 x 100  =  105

Find the HCF of 60, 75 and 105.

HCF (60, 75, 105)  =  Product of common factors

=  3 x 5

=  15

Divide the HCF 15 by 100.

15 / 100  =  0.15

So, the highest common factor of 0.6, 0.75 and 1.05 is

0.15

Example 4 :

Find the LCM of 0.48, 0.72 and 0.108. 

Solution :

In 0.48, 0.72 and 0.108, we have more number of digits after the decimal point in 0.108. That is 3.  

Multiply the given numbers by 1000 to get rid of the decimal point.

0.48 x 1000  =  480

0.72 x 1000  =  720

0.108 x 1000  =  108

Find the LCM of 480, 720 and 108.

LCM (480, 720, 108)  =  Product of all prime factors

=  2 x 2 x 3 x 2 x 2 x 5 x 3 x 2 x 3

=  4320

Divide the LCM 4320 by 1000.

4320 / 1000  =  4.32

So, the least common multiple of 0.48, 0.72 and 0.108 is

4.32

Example 5 :

Find the HCF and LCM of 0.6, 1.5, 0.18 and 3.6. 

Solution :

In  0.6, 1.5, 0.18 and 3.6, we have more number of digits after the decimal point in 0.18. That is 2.  

Multiply the given numbers by 100 to get rid of the decimal point.

0.6 x 100  =  60

1.5 x 100  =  150

0.18 x 100  =  18

3.6 x 100  =  360

Highest Common Factor :

HCF (60, 150, 18, 360)  =  Product of common factors

=  2 x 3

=  6

Divide the HCF 6 by 100.

6 / 100  =  0.06

So, the highest common factor of 0.6, 1.5, 0.18 and 3.6 is

0.06

Least Common Multiple :

LCM (60, 150, 18, 360)  =  Product of all prime factors

=  2 x 3 x 5 x 3 x 2 x 2 x 5

=  1800

Divide the LCM 1800 by 100.

1800 / 100  =  18

So, the least common multiple of 0.6, 1.5, 0.18 and 3.6 is

18

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