Explanation:

Let the L.C.M Be 'L' and H.C.F be 'H'.

L + H = 312 ------------> (i)

L - H = 264 ------------>(ii)

By (i) and (ii) :-

L = 288

H = 24

Sum of the numbers is 168.

The Numbers must be 24x and 24y since the H.C.F is 24.

So 24x + 24y = 168

(x + y) = 7

Possible Values of x and y for which the L.C.M of these numbers will be 288 :-

(3,4)  or it can be taken as (4,3).

Hence the numbers are 24*3 = 72 and 24*4 = 96.