What is the difference between two numbers if their LCM is 630 and HCF is 9 and the sum of the two numbers is 153?

Given GCD of two numbers is 9 and LCM is 630.

Let a, b be two numbers
As we know,

LCM × HCF = The product of given numbers

a×b=9×630
Given a+b=153
By using formula
(a-b)^2=(a+b)^2-4×a×b
(a-b)^2=(153^2)-(4×9×630)
(a-b)^2=729
x-y=27
Ans.27

Another Solution:

Let's assume the numbers are 9*a and 9*b (as the hcf is 9).

As we know,

LCM × HCF = The product of given numbers

So, (9*a)*(9*b) = 630*9

So, a*b = 70
Again 9*(a + b)= 153

By solving those two equations, we get either a=10, b=7 or a=7 , b=10
So either way, the two numbers are 90 and 63.

So, $(\mathrm{90}-\mathrm{63})=27$ or the difference between the two numbers is 27.

Ans.27