A floor of a big hall has dimensions 30 m 60 cm and 23 m 40 cm. It is to be paved with square tiles of the same size. What is the minimum number of tiles required?

To solve this problem, we need to find the greatest common divisor (GCD) of the length and width of the hall in centimeters, which will give us the side length of the largest square tile that can be used. Then, we divide the total area of the hall by the area of one tile to find the minimum number of tiles required.

Step 1: Convert the dimensions of the hall to centimeters. The length of the hall is 30 m 60 cm = 3060 cm. The width of the hall is 23 m 40 cm = 2340 cm.

Step 2: Find the GCD of 3060 and 2340. The GCD of 3060 and 2340 is 60 cm. This is the side length of the largest square tile that can be used.

Step 3: Calculate the area of one tile. The area of one tile is side length * side length = 60 cm * 60 cm = 3600 cm^2.

Step 4: Calculate the total area of the hall. The total area of the hall is length * width = 3060 cm * 2340 cm = 7152000 cm^2.

Step 5: Divide the total area of the hall by the area of one tile to find the minimum number of tiles required. The minimum number of tiles required is total area / area of one tile = 7152000 cm^2 / 3600 cm^2 = 1986.67.

Since we can't have a fraction of a tile, we round up to the nearest whole number. So, the minimum number of tiles required is 1987.