Minimize the bases P and Q such that each of the following alphanumeric equations has at least one solution:

(A) (GO)_{Base P} + (GO)_{Base P} = (GIG)_{Base P}

(B) (GO)_{Base Q}*(GO)_{Base Q} = (GIG)_{Base Q}

Note: Solve each of the alphanumeric equations separately and remember G, O and I must be distinct and G can't be zero.