Question

LCM of two quantities is xy times of their HCF. if one of them is x2-xy and hcf is x-y then find the other quantities

Answer 1

HCF = (x-y)
LCM of two quantities is xy times of their HCF
so LCM = xy(x-y) 

one number = x²-xy = x(x-y)
let the other number be a.

since product of numbers is equal to product of their LCM and HCF

$product\ of\ numbers=HCF*LCM\\ \\(x(x-y))*a=(x-y)(xy(x-y))\\ \\(x(x-y))*a=xy(x-y)^2\\ \\a= \frac{xy(x-y)^2}{x(x-y)} \\ \\a=\boxed{y(x-y)}$

So other number is y(x-y)

Answer 2

product of two nos=HCF X LCM
x²-xyX 2nd no= (x-y)Xxy(x-y)
⇒2nd no=(x-y)(x-y)xy/x(x-y)
⇒2nd no=xy-y²