Step-by-step Solution:

Quick Solution

To form the smallest possible square from rectangular tiles, the side length of that square must be the first number that is a multiple of both dimensions of the tile. This is known as the Least Common Multiple (LCM).

1. Find the Side Length of the Square (LCM)

- The dimensions of one tile are 16 and 24.
- We need to find the LCM of 16 and 24.

• Multiples of 16: 16, 32, 48, 64, ...
• Multiples of 24: 24, 48, 72, ...

The smallest square that can be formed will have a side length of 48 units.

2. Calculate the Number of Tiles Needed

Now, we can determine how many tiles are needed to create this 48x48 square:

• Tiles needed for the length: Side of Square ÷ Length of Tile = 48 ÷ 24 = 2 tiles.
• Tiles needed for the width: Side of Square ÷ Width of Tile = 48 ÷ 16 = 3 tiles.

To form the complete square, we will need a grid of 2 tiles by 3 tiles.

Total number of tiles = 2 × 3 = 6 tiles.

Final Answer: The minimum number of tiles required is 6.