Incidentally, the example of roman numeral multiplication you chose is actually fairly easy. Just break it up as (XI×V) + (XI×I). Then since X×V=L and I×V=V (Romans would have these memorised just like we memorise multiplication tables for all the decimal digits) so the first multiplication is LV and the second is XI, which add to give LXVI by simply interleaving the letters.
That example works well because you don't have to do V * V. You can do XVI * VI = (X + V + I) * (V + I) = (XV) + (XI) + (VV) + (VI) + (IV) + (II) = L + X + XXV + V + V + I = LXXXVVVI = LXXXXVI, which "simplifies" to XCVI, but it's already a good bit messier.
