Question

find lcm and hcf of the following pairs of integers and verify that lcm × hcf = product of the two number 510 and 92

Answer 1

Prime factorization of 510 and 92=
510= 2*3*5*17
92=2*2*23

HCF= 2
LCM=2^2*3*5*17*23=23460


LCM *HCF= 510*92
2*23460=510*92
46920=46920
HENCE, PROVED.

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Answer 2

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

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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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