HCF AND LCM OF FRACTIONS 

The formulas given below can be used to find the highest common factor (HCF) and least common multiple (LCM) of fractions. 

Example 1 :

Find the HCF of : 

3/5 and 7/10

Solution :

Formula to find the highest common factor (HCF) of fractions :

=  HCF of Numerators / LCM of Denominators

HCF of numerators (3, 7)  =  1

LCM of denominators (5, 10)  =  10

Highest common factor (HCF) of 3/5 and 7/10 is 

=  1/10

Example 2 :

Find the HCF of : 

8/21 and 6/35

Solution :

Formula to find the highest common factor (HCF) of fractions :

=  HCF of Numerators / LCM of Denominators

HCF of numerators (8, 6)  =  2

LCM of denominators (21, 35)  =  105

Highest common factor (HCF) of 8/21 and 6/35 is 

=  2/105

Example 3 :

Find the HCF of :

4/5, 3/10 and 7/15

Solution :

Formula to find the highest common factor (HCF) of fractions :

=  HCF of Numerators / LCM of Denominators

HCF of numerators (4, 3, 7)  =  1

LCM of denominators (5, 10, 15)  =  30  

HCF  of (4/5, 3/10, 7/15) is 

=  1/30

Example 4 :

Find the HCF of :

1/2, 3/4, 5/6, 7/8 and 9/10

Solution :

Formula to find the highest common factor (HCF) of fractions :

=  HCF of Numerators / LCM of Denominators

HCF of numerators (1, 3, 5, 7, 9)  =  1

LCM of denominators (2, 4, 6, 8, 10)  =  120  

HCF  of (1/2, 3/4, 5/6, 7/8, 9/10) is 

=  1/120

Example 5 :

Find the LCM of :

3/5 and 7/10

Solution :

Formula to find the least common multiple (LCM) of fractions :

=  LCM of Numerators / HCF of Denominators

LCM of numerators (3, 7)  =  21

HCF of denominators (5, 10)  =  5

Least common multiple (LCM) of 3/5 and 7/10 is 

=  21/5

Example 6 :

Find the LCM of :

8/21 and 6/35

Solution :

Formula to find the least common multiple (LCM) of fractions :

=  LCM of Numerators / HCF of Denominators

LCM of numerators (8, 6)  =  24

HCF of denominators (21, 35)  =  7

Least common multiple (LCM) of 8/21 and 6/35 is 

=  24/7

Example 7 :

Find the LCM of :

2/5, 3/10 and 4/15

Solution :

Formula to find the least common multiple (LCM) of fractions :

=  LCM of Numerators / HCF of Denominators

LCM of numerators (2, 3, 4)  =  12

HCF of denominators (5, 10, 15)  =  5

LCM  of (2/5, 3/10, 4/15) is 

=  12/5

Example 8 :

Find the LCM of :

1/3, 5/6, 5/9 and 10/27

Solution :

Formula to find the least common multiple (LCM) of fractions :

=  LCM of Numerators / HCF of Denominators

LCM of numerators (1, 5, 5, 10)  =  10

HCF of denominators (3, 6, 9, 27)  =  3

LCM  of (1/3, 5/6, 5/9, 10/27) is 

=  10/3

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