Welcome to the forum (despite your apocryphal nomenclature
The H&R Model 48 shotgun was in production (or at least catalogued by H&R) from 1943 to 1957 when it was replaced by the Model 58. The 48 was the result of improvements made to the Model 1908 which became the Model 08 STANDARD.
Value will depend upon condition (as well as, to a lesser degree, on chambering, 16 ga. not being the most popular) - and current RETAIL values will vary from a high of around $125 for an excellent condition 12 ga down to around $50 or less for a parts gun (I've seen some sell for $10 to $25 at live auctions). 20 ga and .410 bore bring a premium of about $10 to $20.
The serial number you cite is very interesting. This model would typically have a letter prefix to the serial number of 'D' for 1943 to 'T' for 1957. I've not seen one of these with a double letter prefix and 'CM' makes no sense in the conventional manner.
Unless your gun has some uncatalogued special features or you are misreading the prefix letters (I know, this is unlikely and almost never happens
) I have no explanation for it being there - therefore I can't really date your piece. There are two recognized variations: 1st (1943-1953) the receiver is "color case hardened" - looks like multicolor tigger stripes; and 2nd (1954-57) the receiver was blued. In either case, the catalogues only list the 16 ga chambering as 2 3/4" - so that is the ammo I'd suggest you use in your gun.
Got a pic of the serial number, by any chance? I would love to see it and add it to my research files, if you don't mind?