Final answer:
The minimum number of 6 by 4 rectangular tiles needed to create a square is 6. This is calculated using the Least Common Multiple of the tile dimensions to form the sides of the square, which are of equal length.
Step-by-step explanation:
To determine the minimum number of 6 by 4 rectangular tiles needed to create a square, we first need to figure out the dimensions that would allow these tiles to be arranged without overlapping and form a perfect square. The key is to find a common multiple of the tile's length and width that can be used to form the sides of the square.
The dimensions of each tile are 6 inches in length and 4 inches in width. To form a square, both dimensions of our square need to be equal, and they also need to be a common multiple of 6 and 4. The smallest common multiple of 6 and 4 is 12. Therefore, we can conclude the side of the square must be at least 12 inches to accommodate whole tiles.
By creating a square with a side length of 12 inches, we would need two tiles along one side and three tiles along the other side, since 12 is divisible by both 4 and 6. So, the total number of tiles used would be 2 multiplied by 3, which equals 6 tiles.
This solution utilizes the concept of Least Common Multiples (LCM) to determine the dimensions that allow for the rectangular tiles to fit perfectly into a square arrangement.