Question

100 Points for Class 10 math

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

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1) 26 and 91 

26 = 2 × 13
91 = 7 × 13

LCM = 2 × 7 × 13
=182

HCF = 13 

→ Verify LCM × HCF = Product of the two numbers

LCM × HCF = 2366
182 × 13 = 2366
2366 = 2366

Therefore, LCM × HCF = Product of the two numbers

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2) 336 and 54

336 = 2 × 2 × 2 × 2 × 3 × 7 
54 = 2 × 3 × 3 × 3

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7
= 3024

HCF = 2 × 3
=6

→ Verify LCM × HCF =Product of the two numbers

LCM × HCF = 18144
3024 × 6 = 18144

Therefore, LCM × HCF = Product of the two numbers

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Answer 2

(1) 26 and 91
Prime factors of 26 = 2 x 13
prime factors of 91 = 7 x 13
HCF { 26, 91 } = common factors of 26 and 91
= 13
LCM { 26, 91 } = 2 x 7 x 13 = 182

Verification :
LCM x HCF = 182 x 13 = 2366
Product of 26 and 91 = 26x91 = 2366
hence,
LCM x HCF = product of numbers

2) 336 and 54
prime factors of 336 = 2 x 2 x 2 x 2 x 3 x 7
Prime factors of 54 = 2 x 3 x 3 x 3
Common factors = 2 x 3 = 6
HCF { 336, 54} = 6

LCM{336, 54} = 2^4 x 3^3 x 7 = 3024
Verification :
LCM x HCF = 6 x 3024 = 18144
Product of 336 and 54 = 18144
Hence,
LCM x HCF = product of numbers