L.C. Smith's take a bad rap for having cracks behind the locks. Most of this is from shooting the wrong type of shells through them over the years.
In looking for a 20 ga., anything before the mid 1930's will be chambered 2 1/2", and any that might have been made in the factory with 2 3/4" chambers will have Chambered 2 3/4 Inches in an oval on barrel flat.
Guns made later in the 30's will have 2 3/4 inch chambers and will be stamped as such.
16 ga. were chambered 2 9/16" and the bores were .650. The bores in later guns were .662 and in the late 30's the chambers were also lengthened to 2 3/4" and will so be marked on barrel flat.
Stan if the gun in your picture is a 16 ga with 32" barrels you have a rare one. Not many 20's or 16's with 32" barrels out there.