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.

Given: Length = 18 m 72 cm

Breadth = 13 m 20 cm

To find: The least number of tiles

Concept Used:

Euclid's division lemma:

If there are two positive integers a and b,

then there exist unique integers q and r such that,

a = bq + r where 0 ≤ r ≤ b.

Explanation:

Length of the courtyard
= 18 m 72 cm
= [18(100) + 72] cm [As, 1 m = 100 cm]
= 1872 cm

The breadth of the courtyard
= 13 m 20 cm
= [13(100) + 20] cm
= 1320 cm

To find the maximum edge of the tile we need to calculate HCF of length and breadth,

Using Euclid’s division lemma:

1872 = 1320 × 1 + 552
As 'r' is not equals to 0,
So apply Euclid’s division lemma on 1320 and 552,

1320 = 552 × 2 + 216

As 'r' is not equals to 0,
So apply Euclid’s division lemma on 552 and 216,
552 = 216 × 2 + 120

As 'r' is not equals to 0,
So apply Euclid’s division lemma on 216 and 120,
216 = 120×1 + 96

As 'r' is not equals to 0,
So apply Euclid’s division lemma on 120 and 96,
120 = 96 ×1 + 24

As 'r' is not equals to 0,
So apply Euclid’s division lemma on 96 and 24,
96 = 24 × 4 + 0

Therefore, HCF of 1872 and 1320 is 24
Maximum edge can be 24 cm.

Number of tiles = = = 4290 tiles