How did the Romans multiply their numerals?

Ems - Thinking about how we multiply today can be helpful answering this question too - there's many methods and they often vary by region so there may be no definitive answer BUT it seems likely that they used a method of doubling and halving which is very straightforward and there is evidence it was used in Egyptian times from the Rhind papyrus (probably worth discussing this method eg 37x39 (ignore odds as remainders) so doubling and having gives 18x78, doing again gives 9x156 and then 4x312 and 2x624 and finally 1x1248 and to get the final answer we 'cast out' any of those with both numbers even (eg 18x78) and total the RHS of the rest which gives 1443 - it might seem complex to us but it is a binary approach really and only appears tricky because we do not always use this approach - familiarity arguably bring fluency and speed - this doubling and halving is used elsewhere eg also known as Russian method or Russian peasants method.

Will - It seemed to work well for them, didn't it?

Ems - Romans are believed to have tended to often write III for 4 than IV - evidence on their remaining  inscriptions- so doubling and halving was perhaps easier than we thought. But as always, getting the answer is key rather than the method and clearly Romans could perform great feats of engineering so their methods worked.