The HCF and LCM of two numbers are 8 and 48 respectively. If one of the number is 24, then the other number is:

Options

A. 48
B. 36
C. 24
D. 16

Answer

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

\[ \text{HCF} \times \text{LCM} = n_1 \times n_2 \]

Where:
- HCF is the highest common factor
- LCM is the least common multiple
- \( n_1 \) and \( n_2 \) are the two numbers

Given:
- HCF = 8
- LCM = 48
- \( n_1 = 24 \) (one of the numbers)

We need to find \( n_2 \) (the other number).

### Step-by-step Solution:

1. **Write down the formula**:
\[ \text{HCF} \times \text{LCM} = n_1 \times n_2 \]

2. **Substitute the known values into the formula**:
\[ 8 \times 48 = 24 \times n_2 \]

3. **Calculate the left side**:
\[ 8 \times 48 = 384 \]
So we have:
\[ 384 = 24 \times n_2 \]

4. **Solve for \( n_2 \)**:
Divide both sides by 24:
\[ n_2 = \frac{384}{24} \]

5. **Calculate \( n_2 \)**:
\[ n_2 = 16 \]

Thus, the other number is **16**.