The HCF and LCM of

8
9

,

10

27

and

16

81

is ____ and ____ respectively.

Question

The HCF and LCM of

8
    9
   
   ,
    
     10
    
     27

and

16
    
     81

is ____ and ____ respectively.

Accepted Answer

The HCF and LCM of

8
    9
   
   ,
    
     10
    
     27

and

16
    
     81

is

2
    
     81

and

80
    9

respectively.Now, the HCF and LCM of fractions is given as follows,

HCF of fractions =
    
      HCF of Numerators 
    
      LCM of Denominators

LCM of fractions =
    
     LCM of Numerators 
    
     HCF of Denominators

We first do the prime factorisation of the numerators and denominators of all the three fractions.

8=2×2×2

10=2×5

16=2×2×2×2

9=3×3

27=3×3×3

81=3×3×3×3

Therefore, we have, LCM (8, 10, 16) =

2
    4
   
   ×5
 HCF (8, 10, 16) =

2
 LCM (9, 27, 81) =

3
    4

HCF (9, 27, 81) =

3 x 3
 Now, as per the formula, we have,

HCF

8
          9
         
         ,
          
           10
          
           27
         
         ,
          
           16
          
           81

=
        
         HCF(8,10,16) 
        
         LCM(9,27,81)

=
        2

3
          4

=
        2
        
         81

So, the HCF is

2
    
     81

.

LCM

8
          9
         
         ,
          
           10
          
           27
         
         ,
          
           16
          
           81

=
        
         LCM(8,10,16) 
        
         HCF(9,27,81)

=

2
          4
         
         ×5
        
         3×3

=
        
         2×2×2×2×5
        
         3×3

=
        
         80
        9

The LCM is

80
    9

.Hence, the HCF and LCM of

8
    9
   
   ,
    
     10
    
     27

and

16
    
     81

is

2
    
     81

and

80
    9

respectively.

The HCF and LCM of $89, 1027$ and $1681$ is and respectively.

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The HCF and LCM of 8 9 , 10 27 and 16 81 is ____ and ____ respectively.

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The HCF and LCM of $89, 1027$ and $1681$ is and respectively.