Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
📚 Submitted Answer
Solution:
(i)
Prime Factorization:
26 = 2 × 13
1 = 7 × 13
HCF:
The common factor is 13.
LCM:
2 × 7 × 13 = 182
Verification:
HCF × LCM = 13 × 182 = 2366
26 × 91 = 2366 ✅
Thus, the product of two numbers = LCM × HCF
(ii)
Prime Factorization:
510 = 2 × 3 × 5 × 17
92 = 2 × 2 × 23
HCF:
The common factor is 2.
LCM:
2 × 3 × 5 × 17 × 23 = 23460
Verification:
HCF × LCM = 2 × 23460 = 46920
510 × 92 = 46920 ✅
Thus, the product of two numbers = LCM × HCF
(iii)
Prime Factorization:
336 = 24 × 3 × 7
54 = 2 × 33
HCF:
The common factors are 2 and 3, so HCF = 2 × 3 = 6
LCM:
24 × 33 × 7 = 3024
Verification:
HCF × LCM = 6 × 3024 = 18144
336 × 54 = 18144 ✅
Thus, the product of two numbers = LCM × HCF
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