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

Answer 1

Let the two numbers be a and b.

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

Then,

HCF$(a,b)$ =1

LCM$(a,b)$=ab

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

Then,

HCF $(a,b)$=1

LCM$(a,b)$=ab

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

Then,

HCF$(a,b)$=1or any other highest common integer

LCM $(a,b)$=ab

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

Then,

HCF$(a,b)$=k

LCM $(a,b)$=k

Hence the correct choice is (d).