LCM of two number x and y is 204 times of their HCF.  If their HCF is 12 and the difference between the number is 60, then the numbers are?

204, 144

a and b are coprime factor of two numbers.

⇒ [LCM = HCF × (ab)]

⇒ LCM = HCF × 204                        

⇒ ab = 204

Now, HCF = 12 and Numbers are 12a and 12b.

ATQ,

12a - 12b = 60

a - b = 5

We can conclude here: a = 17 & b = 12                 [17 × 12 = 204 & 17 - 12 = 5]

Therefore, Numbers are ⇒ 17 × 12, 12 × 12

                                      ⇒ 204, 144