If I've understood the question correctly (and I might well not have!), it can be re-phrased as follows:
Assume I have two arbitrarily chosen integers, n and m.
Find another integer x such that for any integer, p, say, greater than or equal to x, that integer can be expressed as a sum of multiples of n and m. i.e. p = u*n + v*m, where u and v are positive integers (or one of them is zero).
If my interpretation is correct, then
(a) if n and m are both even, there is no such x, since one can never find values of u and v such that u*n + v*m = p when p is an odd number.
(b) If one or both of n and m is/are odd, then I speculate that x = n*m (but I've no proof, and I haven't tried hard to find a counter-example!).
