I might be wrong but, IIRC, the bore dia is a couple of thousands different in the 22LR and 22Mag in most guns, I don't remember which is the largest. This may create a accuracy problem with one of them. In the Gun Digest it has both the 22LR and the 22Mag listed at 26,000 pressure, both are the same, according to GD.
The 223 is a lot higher operating pressure at over 42,000,,,,,Very bad idea just as some have said previously, definately to much for a 22 rim fire bbl.
HM