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A rectangular courtyard is 20m 16 cm long and 15m 60 cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.
Given:
A rectangular courtyard is 20m 16 cm long and 15m 60 cm broad.
It is to be paved with square stones of the same size
To do: Find the least possible number of such stones.
Solution:
Length of the rectangular court yard= $20 m \ 16 cm$
= $(2000 + 16) cm = 2016cm$
Breadth of rectangular court yard= $15 m \ 60 cm$
= $(1500 + 60) cm = 1560 cm$
Least side of the square stones used to pave the rectangular court board = HCF of $(2016, 1560)$

Prime factorization of 2016 = $2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7$
Prime factorization of 1560 = $2 \times 2 \times 2 \times 3 \times 5 \times 13$
HCF $(2016, 1560)$ = $2 \times 2 \times 2 \times 3 = 24$
∴ Side of the square s tones used to pave the rectangular court yard= 24 cm
Least possible number of stones to be paved
= Area of a rectangular courtyard ÷ Area of a square stone
=$ (2016 \times 1560) ÷ (24)^2$
=$314496 \div 576$ = $5460$
Therefore, the least possible number of such stones are 5460.
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