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 of Courtyard $=18m72cm=1872cm$

Width of courtyard $=13m20cm=1320cm$

Edge of the square which is to be used for paving must be common division of length edge of square

Now,

$HCF$ of $\left(1872\&1320\right)=24cm$

Now area of courtyard $=1872cm\times 1320cm$

$=2471040c{m}^2$

For paving Area of square $=24xm\times 24cm$

$=576c{m}^2$

Required number of tiles $=\frac{\text{Area of courtyard}}{\text{Area of square tile}}$

$=\frac{2471040}{576}$

$=4290$ tiles

Hence, no of tiles required $=4290$