Is modulus really necessary in LCG implementations

I need a 32 and 64 bit PRNG and have decided to use LCG. Most implementations are either:

X = (aX + c) mod m or
X = (aX + c) and m

But is the m really necessary? If my X is a uint32 and uint64 respectively wouldn't the data type handle any wrapping for me automatically without me having to explicitly use a mod or an and? As per my implementation below.

#ifdef X32

    uint32 state = seed;
    uint32 a = 1103515245;
    uint32 c = 12345;

#else

    uint64 state = seed;
    uint64 a = 2862933555777941757;
    uint64 c = 3037000493;

#endif

    state = a * state + c;