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Question

The LCM and HCF of two rational numbers are equal, then the numbers must be

(a) prime
(b) co-prime
(c) composite
(d) equal


Solution

Let the two numbers be a and b.

(a) If we assume that the a and b are prime.

Then, 

HCF

LCM

(b) If we assume that a and b are co-prime.

Then, 

HCF

LCM

(c) If we assume that a and b are composite.

Then, 

HCFor any other highest common integer

LCM

(d) If we assume that a and b are equal and consider a=b=k.

Then, 

HCF

LCM

Hence the correct choice is (d).


Mathematics
RD Sharma (2014)
Standard X

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