Arectangular 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