Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the two numbers.
1) 26 and 91
2) 510 and 92
3) 336 and 54

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.