Find the least number of square tiles required to pave the floor of a room $15\text{m }17\text{cm}$ long and $9\text{m }2\text{cm}$ broad.

Convert the dimensions of the room into centimeters:
$$\text{Length}=15\text{m }17\text{cm}=1517\text{cm}$$
$$\text{Breadth}=9\text{m }2\text{cm}=902\text{cm}$$
To find the largest possible size of a square tile, compute the Highest Common Factor ($\text{HCF}$) of $1517$ and $902$:
$$1517=902\times 1+615$$
$$902=615\times 1+287$$
$$615=287\times 2+41$$
$$287=41\times 7+0$$
$$\text{HCF}=41\text{cm}$$
So, the side length of each square tile is $41\text{cm}$.Calculate the minimum number of tiles required:
$$\text{Number of tiles}=\frac{\text{Area of the floor}}{\text{Area of one tile}}=\frac{1517\times 902}{41\times 41}$$
$$\text{Number of tiles}=\left(\frac{1517}{41}\right)\times \left(\frac{902}{41}\right)=37\times 22=814$$