A rectangular courtyard is 18m72cm long and 13m20cm broad. It is to be paved with square tiles of the same size. Find the least possible no. of such tiles?

Given length of rectangular courtyard = 18 m 72 cm = 1872 cm

Width of rectangular courtyard = 13 m 20 cm = 1320 cm

To find the square tile of maximum side we take the HCG of 1872 and 1320

By Euclids division lemma we have

1872 = 1320 * 1 + 552

1320 = 552 * 2 + 216

552 = 216 * 2 + 120

216 = 120 * 1 + 96

120 = 96 * 1 + 24

96 = 24 * 4 + 0

Hence the HCF is 24

Therefore maximum side of the square = 24 cm

Number of tiles required = (Area of rectangular courtyard) / (Area of square tile)

= (1872 * 1320) / (24 * 24)

= 4290