FWIW: Of many things I've tried to improve on Anonymous Monk's gcm(), the only thing that has worked is this:

U64 gcm4( U64 max, U64 n ) {
    U64 c, lcm;

    for( c = 1; ( ~n & 1 ) && ( c < 12 ); ++c ) n >>= 1;
    lcm = n * 4096;
    return ( max / lcm ) * lcm;
}
[download]

Incrementing seems to be fractionally faster than shifting:

anonyM:  gcm for s=2147483648 & r=1 to 1073741824 took:33.850345514550
+  ### original
anonyM: gcm4 for s=2147483648 & r=1 to 1073741824 took:33.590549831120
+  ### my tweak
[download]

But the difference, 1/4 second on > 1 billions calls is so minimal (0.2 nanoseconds), and the shifting better captures the semantics, I've stuck with the original.