The AUG HBAR had the smallest clip of the LMGs in MW2 with 42 rounds. The rest had 100 round clips. The LMG with the smallest clip in this game is the Chainsaw with 80 rounds.
The easiest way to earn this challenge is to fire your LMG into an enemy helicopter, in particular the Helo Pilot since it flies a bit lower to the ground then the Attack Chopper (and its also a bit slower). Yes, this counts as an enemy. You could also try finding a bad Recon Juggernaut and unloading into it as well.