La360 and 727

Big block, small block, and slant 6 all use different bellhousing bolt patterns. You need a smallblock 727.
Input splines were different between standard 727s and ones with a lockup convertor (late 70s-early 80s?). Output splines are all the same, as is the overall length.
Stay away from '65 and earlier transmissions- output used a flange for a ball and trunnion, had cable shift, and a different speedo drive.
Also some HD truck and motorhome trannies had a stubby tailshaft, and/or a flanged output or parking brake drum- but those are readily obvious.
More importantly, most smallblock 727s will have a neutral balanced convertor- your 360 requires an externally balanced (LA 360 only) convertor, or an aftermarket externally balanced flexplate.