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1) 26 and 91

2) 510 and 92

3) 336 and 54

Answer :

1.26 and 91

\(26 = 2 × 13\)

\(91 = 7 × 13\)

HCF = 13

LCM = \(2 × 7 × 13 = 182\)

Product of two numbers 26 and 91 = \( 26 × 91 = 2366\)

HCF × LCM = \(13 × 182 = 2366\)

Product of two numbers is HCF × LCM, so it is verified.

2.510 and 92

\(510 = 2 × 3 × 5 × 17\)

\(92 = 2 × 2 × 23\)

HCF = 2

LCM = \(2 × 2 × 3 × 5 × 17 × 23 = 23460\)

Product of two numbers 510 and 92 = \( 510 × 92 = 46920\)

HCF × LCM = \(2 × 23460 = 46920\)

Product of two numbers is HCF × LCM, so it is verified

3.336 and 54

\(336 = 2 × 2 × 2 × 2 × 3 × 7 = 2^4 + 3 + 7\)

\(54 = 2 × 3 × 3 × 3 = 2 × 3^3\)

HCF = \(2 × 3 = 6\)

LCM = \(2^4 × 3^3 × 7 = 3024\)

Product of two numbers 336 and 54 = \( 336 × 54 = 18144\)

HCF × LCM = \(6 × 3024 = 18144\)

Product of two numbers is HCF × LCM, so it is verified.

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