The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is:

Options

A. 126
B. 144
C. 198
D. 238

Answer

To find the other number when the HCF and LCM of two numbers are given, we can use the relationship between them. The product of the HCF and LCM of two numbers is equal to the product of the two numbers.

Given:
- HCF (Highest Common Factor) = 18
- LCM (Lowest Common Multiple) = 378
- One number (let's call it N1) = 54
- The other number (let's call it N2) = x (unknown)

We can use the formula:
\[ \text{HCF} \times \text{LCM} = N1 \times N2 \]

### Step-by-Step Solution:

1. **Write down the relationship**:
\[ \text{HCF} \times \text{LCM} = N1 \times N2 \]
Plugging in the values:
\[ 18 \times 378 = 54 \times x \]

2. **Calculate the left side**:
\[ 18 \times 378 = 6804 \]
So we have:
\[ 6804 = 54 \times x \]

3. **Solve for x**:
To find x, divide both sides by 54:
\[ x = \frac{6804}{54} \]

4. **Perform the division**:
\[ x = 126 \]

### Conclusion:
The other number is **126**.