The LCIII wasn't quite as common as the LCII, for one thing it cost a bit more than the LCII, but I'd think it was still a bit common. My Dad bought an LCIII back in 1993, and I remember it was several hundred dollars more than an LCII, but with its redesigned logic board optimized for the 68030 CPU, higher RAM ceiling (36MB vs 10MB in the LCII), and faster CPU (25 Mhz vs 16 Mhz), you were getting a lot more computer.

For the record, just about anything that runs on an LCIII should also run on an LCII, however the LCII may have trouble handling some things that the LCIII will handle with ease, due to its low RAM ceiling and/or slower CPU and slower bus. Another software compatibility issue is that the LCII can run System 6.08, whereas the LCIII can't, if thats important to you.