A courtyard is 18 m 72 cm long and 13 m 20 cm wide. What is the least number of identical square tiles needed to pave it completely, without cutting any tile?

Explanation

1. 01

   Fewest tiles means the largest tile. Convert to cm: 1872 cm and 1320 cm.

2. 02

   $1872 = 2^4 \times 3^2 \times 13$ and $1320 = 2^3 \times 3 \times 5 \times 11$, so HCF = $2^3 \times 3 = 24$ cm.

3. 03

   Tiles along the length = $1872 \div 24 = 78$; along the width = $1320 \div 24 = 55$.

4. 04

   Number of tiles = $78 \times 55 = 4{,}290$.