Question

The lcm of two numbers x and y is 204 times their hcf. If their hcf is 12 and the difference between the numbers is 60, then x + y = ?

Answer 1

Answer:

two numbers x=204 y=144

x+y=348

Step-by-step explanation:

Answer 2

The value of x + y is 348.

Step-by-step explanation:

LCM of two numbers x and y = 204 x HCF

HCF = 12

LCM = 204 x 12 = 2448

Product of x and y = LCM x HCF

=> xy = 2448 x 12 = 29376...........(i)

Difference between x and y = x - y = 60................(ii)

$(x+y)^{2} =(x-y)^{2} + 4xy$

Using equation(i) and (ii),

$(x+y)^{2} = (60)^{2} + 4(29376)\\=> (x+y)^{2} = 3600 + 117504 = 121104\\=> x + y = \sqrt{121104} \\=> x + y = 348$

Hence, the value of x + y is 348.