[fgmfgmql] Checking base 10 arithmetic

One can check arithmetic in base 10 by casting out nines, and similarly computing remainders by alternating sums for 11 and the beautiful 1001=7*11*13.  (So 11 is repeated effort.)  We can also get 999=37*27 and prime 101.  Is base 10 especially nice in its ease of checking arithmetic?  We are probably looking for large least common multiple of b^n plus/minus 1, over small n.