Given:
The length of the floor = 12m 48cm
The breadth of the floor = 6m 72cm

To find:
The minimum number of square tiles needed to cover the entire floor.

Method:
To find the minimum number of square tiles needed to cover the floor, we need to divide the floor into equal-sized square tiles and then calculate the number of tiles required.

Step 1: Convert the length and breadth into centimeters
- Length = 12m 48cm = (12 × 100) + 48 = 1248cm
- Breadth = 6m 72cm = (6 × 100) + 72 = 672cm

Step 2: Determine the dimensions of the square tile
- To cover the floor, the square tiles must be of the same size.
- The dimensions of the square tile can be determined by finding the greatest common divisor (GCD) of the length and breadth.
- GCD of 1248 and 672 = 48cm

Step 3: Calculate the number of square tiles needed
- To calculate the number of square tiles needed, divide the length and breadth of the floor by the dimensions of the square tile.
- Number of tiles along the length = 1248 ÷ 48 = 26 tiles
- Number of tiles along the breadth = 672 ÷ 48 = 14 tiles

Step 4: Find the total number of square tiles
- To find the total number of square tiles needed to cover the entire floor, multiply the number of tiles along the length by the number of tiles along the breadth.
- Total number of square tiles = 26 × 14 = 364 tiles

So, a minimum of 364 square tiles of the same size is needed to cover the entire floor.