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Click on your VIN and you will go to a decoder. Click again for the decode, and on page 2 or 3 it says 3.73s for gearing.
Not sure that's right, but otherwise, you will have to crawl under and look for numbers stamped into the housing, driver side front. They may also be a tag on the diff on the back side on one of the cover bolts.
Neither of the previous posts are going to help you since the door tag is missing and the axle information is not encoded in the VIN making any "decoder" will be useless. The decoder will simply give the standard equipment info which may or may not apply to any specific truck.
You'll have to do it the old-fashioned way. Jack up the rear end, put it in neutral, and count the ratio of driveshaft rotations to a wheel rotation. To see if it's an LS or open differential, compare the direction of the rotation of the wheel opposite the one you rotate. Same direction = LS, opposite direction - open diff.
I've never had great luck counting -- it can be difficult to know you went EXACTLY one revolution of pinion and the difference between, say, 3.55 and 3.73 is negligible (although I think your options for a 7.3 truck are 3.55 or 4.10)
I prefer to just pull the diff cover -- the ring gear will be stamped with two numbers separated by a space. One is number of pinion teeth, the other number of ring gear teeth. Divide one into the other and you'll get a result of a common ratio.
If you have a 4wd and the front tag is present you can assume the rear is the same if nothing goes boom in 4wd in a straight line.....