https://rbutterworth.nfshost.com/Tables/romanmult/

How to Multiply Roman Numerals

Preliminaries

I'll assume you know how to read, write, and add roman numerals. If
you can't there's really not much chance of learning how to multiply.

Notation

The ancient Romans didn't use subtractive shorthand notation (e.g. IV
or CM), but allowed four repetitions of a numeral (e.g. IIII or DCCCC
). Calculations will be easier if you do the same. You can wait for
the final answer before normalizing back into modern form.

Parity

Any integer is either odd or even. V and I are odd, and all other
numerals are even, so the parity of a roman numeral can be determined
by looking only at the Vs and Is. An even count of these two numerals
mean even, and an odd count is odd.

Halving

A roman numeral can be halved (i.e. divided by two) by working left
to right using the obvious groupings of numerals. E.g. to find half
of XLVII, treat the XL as XXXX and half of it is XX, and the VII is
half of VI, which is III, with a remainder of I.

Doubling

Similarly doubling can be done right to left using the natural
groupings of numerals. E.g. to double XLII, twice II is IIII, twice 
XL is XXC which is LXXX, and the result is LXXXIIII or LXXXIV.

Multiplication

Make a table with two columns, and enter the two numbers to be
multiplied into the first row. (If you didn't enter them in roman
numerals, enter them as such on the second 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

17   42
XVII XXXXII
VIII   LXXXIIII
IIII   CLXVIII
II     CCCXXXVI
I    DCLXXII
      
     = XXXXIIDCLXXII
     = DCLXXXXXXIIII
     = DCCXIIII
     = DCCXIV
     714

61  14
LXI XIIII
XXX   XXVIII
XV  LVI
VII CXII
III CCXXIIII
I   CCCCXXXXVIII
     
    = XIIIILVICXIICCXXIIIICCCCXXXXVIII
    = CCCCCCCLXXXXXXXXVVIIIIIIIIIIIIII
    = DCCCLIIII
    = DCCCLIV
    854

14    61
XIIII   LXI
VII   CXXII
III   CCXXXXIIII
I     CCCCLXXXVIII
       
      = CXXIICCXXXXIIIICCCCLXXXVIII
      = CCCCCCCLXXXXXXXXXVIIIIIIIII
      = DCCCLIIII
      = DCCCLIV
      854

Division anyone?

Notes

Generally the table will be shorter if the smaller number is in the
left column, though some numbers, even if large, might be better in
the left column if they result in far less addition (e.g. try CXXVIII
).

This method is not limited to Roman Numerals. It will work with any
notation that allows easy doubling, halving, and parity checks.

Content last updated 2011-05-11.