The LCM and HCF of two rational numbers are equal,

Solution:

Let the two numbers be a and b.

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

Then, 

$\operatorname{HCF}(a, b)=1$

$\operatorname{LCM}(a, b)=a b$

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

 

Then, 

$\operatorname{HCF}(a, b)=1$

$\operatorname{LCM}(a, b)=a b$

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

 

Then, 

$\operatorname{HCF}(a, b)=1$ or any other highest common integer'

$\operatorname{LCM}(a, b)=a b$

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

 

Then, 

$\operatorname{HCF}(a, b)=k$

$\operatorname{LCM}(a, b)=k$

Hence the correct choice is (d).