The LCM of two numbers is 112 and their HCF is 2. If one of the number is 14, then find the other number.

Explanation

To find the other number when given the LCM, HCF, and one of the numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between LCM, HCF, and the two numbers**:
The relationship is given by the formula:
\[ \text{LCM} \times \text{HCF} = n_1 \times n_2 \]
where \( n_1 \) and \( n_2 \) are the two numbers.

2. **Identify the known values**:
From the question, we know:
- LCM = 112
- HCF = 2
- One number \( n_1 = 14 \)

3. **Substitute the known values into the formula**:
We can substitute the known values into the formula:
\[ 112 \times 2 = 14 \times n_2 \]

4. **Calculate the left side of the equation**:
First, calculate \( 112 \times 2 \):
\[ 112 \times 2 = 224 \]
So, we have:
\[ 224 = 14 \times n_2 \]

5. **Solve for \( n_2 \)**:
To find \( n_2 \), we can rearrange the equation:
\[ n_2 = \frac{224}{14} \]

6. **Perform the division**:
Now, divide 224 by 14:
\[ n_2 = 16 \]

7. **Conclusion**:
Therefore, the other number is:
\[ n_2 = 16 \]

### Final Answer:
The other number is **16**.

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