If `n^(th)` division of main scale coincides with `(n + 1)^(th)` divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.

Explanation

`(n - 1) v = n s implies v = ((n)/(n + 1)) s`
`LC = s - v = s = ((n)/(n + 1)) s = (s)/(n + 1) = (a)/(n + a)`