At phy6.org:
It is often said that an important advantage of the decimal notation over the Roman one is that makes multiplication of numbers much easier. Adding CLXXVII to XXIII may be relatively straightforward — but how about multiplying the two?
It is indeed easier to multiply these as decimal numbers 177 by 23, but the Romans also had a multiplication method of their own. It was probably discovered by trial and error, and it always worked, though the Romans did not know why.
Here the method is described, and its secret explained…