A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Question

Philoid · Accepted Answer

Length of the courtyard = 1872 cm

Breadth of the courtyard = 1320 cm

To find the size of the tile we need to calculate HCF of length and breadth

Using Euler’s division lemma: a = pq + r where 0≤r

1872 = 1320 × 1 + 552

1320 = 552 × 2 + 216

552 = 216 × 2 + 120

216 = 120×1 + 96

120 = 96 ×1 + 24

96 = 24 × 4 + 0

Therefore HCF of 1872 and 1320 is 24

Number of tile = = = 4290 tiles