How do I find two numbers when I know that their LCM is 36 and HCF is 15?

If the HCF of the two numbers say x and y is 15; the numbers can be represented as following:

x = 15a and y = 15b where a and b are positive integers

It is given that LCM of x and y is 36

Now LCM (x,y) * HCF (x,y) = x * y

Hence, 36 * 15 = 15a * 15b

540 = 225*a*b

or 2.4 = a*b

The product of two integers cannot be 2.4 hence such two numbers do not exist.