A rectangular courtyard is 18m72cm long and 13m20cm broad. It is to be paved with square tiles of same size. Find the least possible number of such tiles.

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Solution

Area = lengthbreadth
=18721320 cm
=247104 cm^2
Find the side length of largest square which tile can be used to floor the rectangular living room of size 1872×1320 cm .
HCF of 1872 and 1320 gives the side length of the largest square.
HCF=
1872 = 13201+552
1320 = 5522 + 216
552 = 2162 + 120
216 = 1201 + 96
120 = 961 + 24
94 = 244 + 0

HCF of 1872 & 1320 is 24

no. of tiles required to floor is (18721320) / (2424)
= 4920

Ans is 4920 tiles

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