Remington has made several versions of the 870. The original 20 gauge was built on the 12 gauge size frame. They have also made a version called the Light Contour (LC), Lightweight (LW) and the Special Field.
The Lightweight and the Special Field are both the smaller framed guns (20 gauge frame), but barrels won't interchange. I'm not sure where the Light Contour fits in the equation, but I don't think barrels for it will interchange with any of the others?
I always thought the LW's were all made in 3" mag, but apparently not. I do know the newer LW's and Express models in 20 ga are all 3" mags and the barrels will interchange.
If your gun was originally a 2 3/4" receiver model (LW) then a 3" barrel should fit (but wait until you hear from someone who knows for sure!). I know guys have done this, but you sould ONLY shoot 2 3/4" shells in it! Remington of course wouldn't tell anyone this because of liability reasons.