Question

100 Points for Class 10 maths


Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers
1) 26 and 91
2) 336 and 54

Answer 1

1. 26 and 91
  26= 2 x 13
  91= 7 x 13
  LCM= 2 x 7 x 13= 182
  HCF= 13

 LCM x HCF = Product of the no. or not?
 182 x 13 = 26 x 91
 => 2366= 2366.
∴ it is true for this question
2. 336 and 54
   336 = 2 x 2 x 2 x 2 x 3 x 7
   54 = 2 x 3 x 3 x 3
   LCM= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7= 3024
   HCF= 2 x 3= 6
   LCM x HCF = Product of the no. or not?
   6 x 3024 = 336 x 54 
=> 18144 = 18144
 ∴ it is true for this question

Answer 2

HI there !

1) 26 and 91

Prime factorization of 26 and 91 :-

26 = 2 × 13
91 = 7 × 13

HCF = 13
LCM = 13 × 2 × 7 = 182

Verification:-

HCF × LCM = 13 × 182 = 2366           ---> [1] 

Product of two no:s = 26 × 91 = 2366               ---> [2] 

From (1) and (2) ,its clear that 

HCF × LCM = Product of two no:s 
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2) 336 and 54

Prime factorization of 336 and 54

336 = 2⁴ × 3 × 7
54  = 3³ × 2

HCF = 2 × 3 = 6 
LCM = 2⁴ × 3³ × 7 = 3024

Verification ,

HCF × LCM =  6 × 3024 = 18144                ---> [1]
Product of 2 no:s = 336 × 54 = 18144           ---> [2]

From (1) and (2) , its clear that 

HCF × LCM = Product of two no:s