Finding the sum of two numbers given the difference of LCM and GCD. 
l-h=57
Let, the two numbers be a and b.
Then,
     ab=lh

How to proceed further? Please give me just hints? They have asked the minimum value of the sum so, I think that I have to take different possibilities.

You want to minimize $lh$ subject to the condition $l-h=57$. So $l=57+h$, and the formula you want to minimize is $lh=(57+h)h$. Since we are looking at natural numbers, this will be the smallest possible when $h=1$, and then $lh=(57+1)\times1=58$. 
