Position Counts With roman numerals, the position of the letters is very important.
IV is not the same as VI, being 4 and 6 respectively. The typical usage is that the letters are listed from left to right, going from higher values to lower values. When a lower value precedes a higher value, the lower value is subtracted from the higher. The example you gave of IVL and LVI both meaning 56 isn't exactly accurate. Either way, our imaginary Roman would shake his head at the ignorance of all those not Roman, because either usage would be very odd.