# How to multiply Roman numerals?

How to multiply Roman numerals? I need an algorithm of multiplication of numbers written in Roman numbers. Help me please.

• Convert to Arabic numerals $\to$ multiply $\to$ convert back. (Half joke) Commented Nov 15, 2015 at 17:04
• without convert!!! Commented Nov 15, 2015 at 17:06
• I've heard a lot about the American humor. Commented Nov 16, 2015 at 19:14

Make a table with two columns, and enter the two numbers to be multiplied into the first row. Make the next row by halving the first number (discarding remainders) and doubling the second. Continue until there is nothing left to halve. Cross out all the rows where the left number is even. Add the remaining numbers in the second column. The result is the product of the first two numbers

Examples

Source

I don't like any on-line solutions to Numeral multiplication so I made one up.

The only thing you need to remember when multiplying is V x V = XXV all other multiple combinations are column shifts

Example: XXVII multiplied by XVIII

XXXVII across the top is multiplied by each individual numeral of XVIII down the left column, then each column is totalled.

$$\begin{matrix} &&&& XXX & V & II \\ X && CCC & L & XX \\ V &&& LLL & XX & V \\ &&&&& VV \\ I &&&& XXX & V & II \\ I &&&& XXX & V & II \\ I &&&& XXX & V & II \\ ---- & ---- & ---- & ---- & ---- & ---- & ---- \\ Carry & D & CCC & LLL & XXX & V \\ : & = & = & = & = & = & = \\ Total & D & C & L & X & V & I \\ \end{matrix}$$

E.g. V (left) x II (top) = VV, carried to V column VxV = XXV and VxXXX = LLL There are 6 I's which total VI the V is carried. 6 V's+that V carry = V + XXX carried

I have resisted the urge to use decimals to convert numerals at each stage, that's your task.

The final result is DCLXVI, a single occurrence of all numerals below M

A revalation perhaps?

All this only takes seconds on an Abacus and my division method is equally different

Take the first number you want to multiply and break it down into parts, any way you choose. E.G. 43 = XLIII = XL + III, or X + X + X + X + III, etc. Do the same with the second number in the multiplication. E.G. 15 = XV = X + V, or V + V + V, etc.

Take any pair of those combinations and set them within a table, with the higher row showing the first number's parts, and the lower row showing the second number's parts. Multiply starting from the lower right to the upper row, then the lower left to the upper row. Place the result to each equation underneath, vertically.
Total them.

It is conversion to Hindu numerals, Not Arabic. Just because Europeans learnt from Arabs does not mean the founders change!

https://rbutterworth.nfshost.com/Tables/romanmult is one place multiplication is explained