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Question

If a=23×34×72and b=23×32×53, then which of the following is true?


A
HCF=23×32;LCM=23×34×53×72
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B
HCF=23×32;LCM=23×32×52×73
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C
HCF=23×32;LCM=23×32×53×73
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D
LCM=22×32;HCF=23×33×53×72
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Solution

The correct option is A HCF=23×32;LCM=23×34×53×72

HCF = Product of the smallest powers of each common prime factor in the numbers.
LCM = Product of the largest powers of each common prime factor in the numbers.
The common prime factors of a and b are 2 and 3.
Thus, HCF=23×32.
All the prime factors of a and b are 2,3,5 and 7.
Thus, LCM=23×34×53×72


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