A rectangular Courtyard is $18m72cm$ long and $13m20cm$ broad it is to be paved with square tiles of the same size and the least possible number of such tiles?

Finding the least number of tiles required:

Given that, Length $=1872cm$

Width $=1320cm$

The edge of the square tile must be the common divisor of the dimensions of the courtyard.

So, the maximum edge of square tile $=$ HCF of $1872$ and $1320=24cm$

So, the required number of tiles $=$ $\frac{areaofcoutyard}{Areaofsquaretile}$

$=$$\frac{1872\times 1320}{{\left(24\right)}^2}$

$=$$4290$

Thus, the least number of tiles required to cover the courtyard is $4290$.