How to tell if greedy algorithm suffices for finding minimum coin change?

The minimum coin change problem is an NP-complete problem but for certain sets of coins the greedy algorithm (choose largest denominations first) works. Given a set of integers denoting coin-values, what's the fastest algorithm to determine if the greedy algorithm suffices or not? One obvious way is to build up your dynamic programming solution till the largest denomination and see for each if it yields a better solution than the greedy way. But is there a faster "math-way" of detecting it?