The LCM of two numbers x and y is 204times their HCF. If their HCF is 12 and thedifference between the numbers is 60,then x + y =?

To solve this problem, we need to use the relationship between the LCM (Least Common Multiple), HCF (Highest Common Factor), and the numbers themselves. The relationship is given by:

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

Given that the LCM is 204 times the HCF, we can substitute these values into the equation:

x * y = 204 * 12 * 12

Solving this gives:

x * y = 29484

We also know that the difference between the two numbers is 60, so we can write:

x = y + 60

Substituting this into the first equation gives:

(y + 60) * y = 29484

Solving this quadratic equation gives two possible values for y: 174 and -170. Since we're dealing with number theory, we discard the negative solution, leaving y = 174.

Substituting y = 174 into x = y + 60 gives x = 234.

Therefore, x + y = 234 + 174 = 408.