It's a late 1980s model, around 1986/1987. There should be two more characters to the serial number, preceding K6288. The first character should be an "N". The 2nd caharacter will be a number indicating the year of manufacture.

The frames for the LeMans RS were typically Tange #2, which is a good, seamless, double butted, chromium-molybdenum tubeset. The forks were often Tange 2001 which was a seamed, double butted, manganese-molybdenum tubeset. I haven't seen an RS with manganese-molybdenum used for the main tubes. Regardless, Tange is the name of the manufacturer. #2 and 2001 are model names/grades of their tubesets. Manganese-molybdem (Mn-Mo) is an alloy that lies between the hi-tensile steels found on entry-leverl bicycles and the chromium molybdenum (Cr-Mo) found on middle and high bicycles. Typically, it was found on lower, mid-range bicycles. The better the tubing, the stronger it is and therefore can be used to produce thinner tubes and a lighter frame.

An RS from this period would have cost $325-$425 US, depending on the year.