Question

Find the hcf and lcm of the following pairs of integers and verify that lcm *hcf =product of the two numbers 1) 510 and 92 2)336 and 54

Answer 1

Answer:

LCM of 510 and 92= 2460

HCF of 510 and 92 =2

hcf ×lcm = product of two numbers

LHS= HCF × LCM

= 2× 2460

= 46920

RHS=510×92

=46920

LHS = RHS

2 LCM= 3024

HCF = 6

hcf ×lcm = product of two numbers

LHS = 3024 × 6

= 18144

RHS = 336 × 54

= 18144

LHS = RHS

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

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(i) 26 and 91

Expressing 26 and 91 as product of its prime factors, we get,

26 = 2 × 13 × 1

91 = 7 × 13 × 1

Therefore, LCM (26, 91) = 2 × 7 × 13 × 1 = 182

And HCF (26, 91) = 13

Verification

Now, product of 26 and 91 = 26 × 91 = 2366

And Product of LCM and HCF = 182 × 13 = 2366

Hence, LCM × HCF = product of the 26 and 91.

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(ii) 510 and 92

Expressing 510 and 92 as product of its prime factors, we get,

510 = 2 × 3 × 17 × 5 × 1

92 = 2 × 2 × 23 × 1

Therefore, LCM(510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460

And HCF (510, 92) = 2

Verification

Now, product of 510 and 92 = 510 × 92 = 46920

And Product of LCM and HCF = 23460 × 2 = 46920

• Hence, LCM × HCF = product of the 510 and 92.

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(iii) 336 and 54

Expressing 336 and 54 as product of its prime factors, we get,

336 = 2 × 2 × 2 × 2 × 7 × 3 × 1

54 = 2 × 3 × 3 × 3 × 1

Therefore, LCM(336, 54) = = 3024

And HCF(336, 54) = 2×3 = 6

Verification

Now, product of 336 and 54 = 336 × 54 = 18,144

And Product of LCM and HCF = 3024 × 6 = 18,144

• Hence, LCM × HCF = product of the 336 and 54.

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