joey79 over at bimmerforums made this entire thread on exchanging the e36 lsd rear differentials into an e21 rear differential case:

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"I finally got around to tearing into my 168mm e36 lsd. Upon attempting to simply swap the e36 internals into the e21 case, it was obvious that it just wasn't going to fit without modification to either the case or the lsd unit. The opening of the e21 case isn't as wide as the e36 case. I didn't want to modify any of the moving parts, so I figured the only way to accomplish the goal was to grind away the portion of the case that was preventing entry of the lsd unit and ring gear. Here are some pictures.


Left: e36 Right: e21

I cut off the speedo sensor wheel on the e36 unit.

The opening on the e21 diff (right) is smaller than the e36. On the e36, the lsd/ring gear unit can be inserted straight in. With the e21 case, the unit must be inserted non ring gear side first, then rotated. A small amount of the case needed to be removed to allow the ring gear to clear.

The opening on the e21 diff (right) is smaller than the e36. On the e36, the lsd/ring gear unit can be inserted straight in. With the e21 case, the unit must be inserted non ring gear side first, then rotated. A small amount of the case needed to be removed to allow the ring gear to clear.

I was concerned that the large o-ring on the side cover wouldn't make a good enough seal with this amount of material removed, but I test fitted the side cover, and it seems to be fine.

LSD unit with ring gear installed with both side covers on.

Now that I know it can physically fit, the rest should be easy enough. I'll have to swap pinion gears. I'll be getting all new bearings, seals and o-rings. If I have problems with gear mesh, I'll take it to a diff builder to shim it properly, but I have all winter to pick at it.

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Update:

I pulled the pinions from the e36 and e21 diffs. I measured them with a digital micrometer, and all measurements were within .002" They are interchangeable.

 E36 is on the left, E21 on the right. The diff is a 3.45 (I believe 25% lock) from an e36 318is.  3.45 LSD would be great for cruising at highway speeds."

i will assume the half shaft will need to be cut and shorten like an inch or 2. or no ?

Source: http://forums.bimmerforums.com/forum/showthread.php?t=1565138&highlight=output+shafts