A) What is meant by the least count of a measuring instrument? b) Find and write the least count of this scale.

The centimeter scale has major markings every 1 cm and minor markings every 1 mm (10 minor divisions per cm).

The inch scale has major markings every 1 inch and minor markings every $\frac{1}{8}$ inch (or $\frac{1}{16}$ inch, but larger than 1 mm).

The smallest division is 1 mm on the cm side.

Least count = 1 mm.

Final answer: Least count = $\boxed{1 \text{ mm}}$