how to tell what type of smith revolver i have

With the L being a "medium large" compared to the slightly smaller K frame.

The whole point of the L frame used on the 586 and 686 and some others was to make the cylinder a hair larger than the K frame gun so that the forcing cone did not need the flat on the lower side. But it's no where near as big as the N frame which comes in sizes from .357 to .45Colt.
 
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