HCF of two numbers is 28 and their LCM is 336. if one number is 112, then the other number is

Options

A. 56
B. 70
C. 84
D. 98

Answer

To find the other number when the HCF of two numbers is 28, their LCM is 336, and one of the numbers is 112, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between HCF, LCM, and the two numbers**:
The relationship between the HCF (Highest Common Factor), LCM (Lowest Common Multiple), and the two numbers (let's call them A and B) is given by the formula:
\[ \text{HCF} \times \text{LCM} = A \times B \]

2. **Substitute the known values**:
We know:
- HCF = 28
- LCM = 336
- One number (A) = 112
We need to find the other number (B). Substituting the known values into the formula gives:
\[ 28 \times 336 = 112 \times B \]

3. **Calculate the left side**:
First, we calculate \(28 \times 336\):
\[ 28 \times 336 = 9408 \]

4. **Set up the equation**:
Now we have:
\[ 9408 = 112 \times B \]

5. **Solve for B**:
To find B, we can rearrange the equation:
\[ B = \frac{9408}{112} \]

6. **Perform the division**:
Now, we divide 9408 by 112:
\[ B = 84 \]

7. **Conclusion**:
Therefore, the other number is:
\[ \text{Other number} = 84 \]

### Final Answer:
The other number is **84**.