# Find the LCM and HCF of the following pair of integers and verify that LCM x HCF = product of the 2 numbers

I) 26 and 91
Ans. 26 = 2 x 13
91= 7 x 13
HCF = 13
LCM = 2 x 7 x 13 = 182
Product of the 2 numbers = 26 x 91 = 2366
HCF x LCM = 13 x 182 = 2366
Hence, product of two numbers = HCF x LCM

II) 510 and 92
510 = 2 x 3 x 5 x 17
92 = 2 x 2 x 23
HCF = 2
LCM = 2 x 2 x 3 x 5 x 17 x 23 = 23460
Product of the two numbers = 510 x 92 = 46920
HCF x LCM = 2 x 23460
= 46920
Hence, product of two numbers = HCF x LCM

III) 336 and 54
336 = 2 x 2 x 2 x 2 x 3 x 7
336 = 24 x 3 x 7
54 = 2 x 3 x 3 x 3
54 = 2 x 3³
HCF = 2 x 3 = 6
LCM = 24 x 3³ x 7 = 3024
Product of the two numbers = HCF x LCM
I) 26 and 91
Ans. 26 = 2 x 13
91= 7 x 13
HCF = 13
LCM = 2 x 7 x 13 = 182
Product of the 2 numbers = 26 x 91 = 2366
HCF x LCM = 13 x 182 = 2366
Hence, product of two numbers = HCF x LCM

II) 510 and 92
510 = 2 x 3 x 5 x 17
92 = 2 x 2 x 23
HCF = 2
LCM = 2 x 2 x 3 x 5 x 17 x 23 = 23460
Product of the two numbers = 510 x 92 = 46920
HCF x LCM = 2 x 23460
= 46920
Hence, product of two numbers = HCF x LCM

III) 336 and 54
336 = 2 x 2 x 2 x 2 x 3 x 7
336 = 24 x 3 x 7
54 = 2 x 3 x 3 x 3
54 = 2 x 3³
HCF = 2 x 3 = 6
LCM = 24 x 3³ x 7 = 3024
Product of the two numbers = HCF x LCM

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