Peecomputing scaled reciprocal is unfeasible for large words. Your lookup table for example with 32-bit words would have 2^32 entries (excluding the reciprocal of 0). That lookup would be enormous.
However for small tables this is feasible so you can build a small table of 256 reciprocals, and then handle the division by group of 4 bits (i.e. work in base 16 and make the traditional division digit by digit in that base, given that you'll handle two digits at once for the product). If you can use a larger lookup table (e.g. 1024 entries, i.e. 10 bits, you'll handle the divisions in base 32; with 4096 entries, the division will be made in base 64; above this limit the lookup table is already too large: 16K entries would turn into a too large module).
But there are other ways to perform divisions than the classic Euclidian method.