The Boeing 747-300 is not a commonly-seen aircraft at LAX; the only one I've seen within the last year has been operated by cargo carrier Southern Air. Even in its heyday, the B743 was not a common aircraft: Boeing only built 81 of the model. The big difference between the -300 and earlier -200 and -100 models is the -300's extended "hump" for the upper deck, which is over 23 feet (7 meters) longer than the previous models'. Dimensions, maximum weights and engines remained pretty much the same between the -200 and -300 models, but improved aerodynamics allowed a slightly higher cruise speed, and the longer upper deck allowed for an additional forty to fifty seats. The -200 continued in production concurrently with the -300, and curiously the -200 was even built for a year or so after -300 production ended in 1990. The -300, which first flew in 1983, was soon replaced by the -400, which was introduced in 1985 and retained the extended upper deck but added wing extensions with winglets. The long hump distinguishes the -300 from the earlier models, and the winglets distinguish the -400 from the -300. Nearly all the B747s seen at LAX these days are -400s, although we do see a few -200s brought in by cargo operators.
Southern Air's new paint scheme, already looking a bit weathered on this B747-300 as it departs off Runway 25 Right. The curious thing is that their website makes no mention of their having a B743; their fleet list shows B742s and B772s, with B744s on the way. That's a United B757-200 being towed in the foreground.
Here is an earlier view of what I believe to be the same aircraft (the registration is not visible in this shot) in its previous Cargo 360 livery. Southern Air was bought by the holding company that owned Cargo 360, and the two operations were merged into the Southern Air that we see today.
Qantas was the last passenger carrier to bring B743's into LAX, and in fact their last B743 revenue flight was a flight from Melbourne to Los Angeles in late December, 2008. One other distinguishing characteristic about the Qantas B747s is that the engine cowlings on their -300s were bare metal, while the -400 cowlings are painted.
This is the only other B747-300 that I've photographed (or recall seeing) at LAX, flown by Saudi Arabian Airlines. These photos were taken several years ago, as evidenced by the Ted Airbus seen in the second shot. Saudi isn't a scheduled operator at LAX, but we do see them from time to time; most recently (last week) in a B777-200. I've also seen them show up in a B747SP, MD11, and L-1011 (the same Tristar I showed you in civilian paint a month or two ago; the casino bought it from Saudi).
Update: Cargo carrier Atlas Air (callsign: Giant) showed up with a B743 a couple of months after this was originally published: