The only solution for the two numbers is: MYM = 363 and AMATYC = 131769.

I have made the following observations so far :

1) M cannot be 0 or 5 or 6, since that would make M = C.

2) M cannot be 1 or 2, as these would result in A = 0.

3) So the pair (M, C) must be among (3, 9), (4, 6), (7, 9), (8, 4), (9, 1).