Question

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

Options

• prime

• co-prime

• composite

• 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)=1`or 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).