N divisions on the main scale of a vernier calipers coincide with...

It is given that& \left(N + 1\right)$~Divisions on vernier scale \left(V . S . D .\right)=N$~Divisions on main scale~ \left(M . S . D .\right)$<br />$⇒ 1V . S . D . = \dfrac{N}{N + 1}M . S . D .$</p><p>Least count of vernier callipers~\left(L . C .\right) = 1M . S . D . - 1V . S . D .$

$⇒ L . C . = a - a\left(\dfrac{N}{N + 1}\right) = \dfrac{a}{N + 1}unit</p>$