LC of main scale = 1 M.S.D
LC of vernier scale = 1 V.S.D
(taken separately)
"...if the main scale is a CM scale with 10 divisions in between (like a normal scale), then its vernier may have 11 divisions squeezed up in that same space..."
In my notation, 10 M.S.D = 11 V.S.D
"..microscopes have main scale having 20 divisions between a cm.. so giving it LC = 0.05cm, and vernier ends up having 51 divisions squeezed up in the place of 2.5 cm ..."
In my notation, 50 M.S.D = 51 V.S.D
^^ The above was to clarify my (shorthand) notation. (As Wikipedia uses the same, I considered them to be standard notations.)
@Mashy
I don't know much about microscopes, but I think they use the concept of a screw gauge.
In case of a Vernier Caliper, I can prove (by elementary mathematics) that LC is less than what you calculated.
For the more common cases (and I think you were trying to refer to these)
9 M.S.D = 10 V.S.D ; LC = 0.1 M.S.D
49 M.S.D = 50 V.S.D ; LC = 0.02 M.S.D