A room `5.44 xx 3.74` m is to be paved with square tiles. The least number of tiles required to cover the floor is ----

Options

A. 162
B. 176
C. 184
D. 192

Answer

To find the least number of square tiles required to cover the floor of a room measuring 5.44 m by 3.74 m, we can follow these steps:

### Step 1: Convert the dimensions of the room to centimeters
Since the dimensions are given in meters, we need to convert them to centimeters for easier calculations.
- 1 meter = 100 centimeters
- Length = 5.44 m = 5.44 × 100 = 544 cm
- Width = 3.74 m = 3.74 × 100 = 374 cm

### Step 2: Find the dimensions of the room in centimeters
- Length = 544 cm
- Width = 374 cm

### Step 3: Calculate the area of the floor
The area of the floor can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
\[ \text{Area} = 544 \, \text{cm} \times 374 \, \text{cm} \]
\[ \text{Area} = 203536 \, \text{cm}^2 \]

### Step 4: Find the side length of the square tile
To minimize the number of tiles, we need to find the largest square tile that can fit into both dimensions of the room. This is done by finding the greatest common divisor (GCD) of the two dimensions (544 cm and 374 cm).

Using the Euclidean algorithm:
1. Divide 544 by 374, which gives a quotient of 1 and a remainder of 170.
2. Now, divide 374 by 170, which gives a quotient of 2 and a remainder of 34.
3. Next, divide 170 by 34, which gives a quotient of 5 and a remainder of 0.

Since the remainder is now 0, the last non-zero remainder (34 cm) is the GCD.

### Step 5: Calculate the area of one tile
The area of one square tile with side length equal to the GCD is:
\[ \text{Area of tile} = \text{Side}^2 = 34 \, \text{cm} \times 34 \, \text{cm} = 1156 \, \text{cm}^2 \]

### Step 6: Calculate the least number of tiles required
Now, we can find the least number of tiles required by dividing the area of the floor by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of floor}}{\text{Area of tile}} \]
\[ \text{Number of tiles} = \frac{203536 \, \text{cm}^2}{1156 \, \text{cm}^2} \]
\[ \text{Number of tiles} = 176 \]

Thus, the least number of tiles required to cover the floor is **176**.

---