A rectangular floor measures 12 m by 20 m. Calculate the size of the largest square tile that can be used to tile the floor, and the number of tiles needed.

$$12 = 2 \times 2 \times 3 = 2^2 \times 3$$ $$20 = 2 \times 2 \times 5 = 2^2 \times 5$$

The common prime factors are $2^2$.

$$\text{GCD}(12, 20) = 2^2 = 4$$

The side length of the maximum size square tile is $4 \text{ m}$.

The required size of each tile is $\boxed{\text{4 m by 4 m}}$.

$$\text{Area of floor} = \text{length} \times \text{width}$$ $$\text{Area of floor} = 20 \text{ m} \times 12 \text{ m} = 240 \text{ m}^2$$

The side length of each tile is $4 \text{ m}$.

$$\text{Area of tile} = \text{side} \times \text{side}$$ $$\text{Area of tile} = 4 \text{ m} \times 4 \text{ m} = 16 \text{ m}^2$$

$$\text{Number of tiles} = \frac{\text{Area of floor}}{\text{Area of tile}}$$ $$\text{Number of tiles} = \frac{240 \text{ m}^2}{16 \text{ m}^2} = 15$$

The number of tiles required is $\boxed{15}$.