AbsoluteTiming[
 f[x_] := Sort@IntegerDigits[x];
 g[x_] := Module[{t = f[x]},
   Return[f[2 x] == f[3 x] == f[4 x] == f[5 x] == f[6 x] == t]];
 ans = NestWhile[# + 1 &, 1, ! g[#] &]]