Question

A rectangular courtyard is 20 m 16 cm long and 15 m 60 cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

Answer 1

Length of the rectangular courtyard = 20 m 16 cm = 2,016 cm
Breadth of the rectangular courtyard = 15 m 60 cm = 1,560 cm
Least possible side of the square stones used to pave the rectangular courtyard = HCF of (2,016 and 1,560)
Prime factorisation of 2,016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
Prime factorisation of 1,560 = 2 × 2 × 2 × 3 × 5 × 13
HCF of (2,016, 1,560) = 2 × 2 × 2 × 3 = 24

Least possible side of square stones used to pave the rectangular courtyard is 24 cm.
Number of square stones used to pave the rectangular courtyard

$=\frac{\mathrm{Area}\mathrm{of}\mathrm{rectangular}\mathrm{courtyard}}{\mathrm{Area}\mathrm{of}\mathrm{square}\mathrm{stone}}=\frac{2016\mathrm{cm}\times 1560\mathrm{cm}}{(24\mathrm{cm}{)}^2}=5460$
Thus, the least number of square stones used to pave the rectangular courtyard is 5,460.