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 and LCM of two numbers are given, we can use the relationship between HCF, LCM, and the two numbers. The relationship states that:

\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

Given:
- HCF = 28
- LCM = 336
- First Number = 112
- Second Number = x (which we need to find)

### Step-by-Step Solution:

1. **Write down the relationship**:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]
Substituting the known values:
\[ 28 \times 336 = 112 \times x \]

2. **Calculate the left side**:
\[ 28 \times 336 = 9408 \]

3. **Set up the equation**:
\[ 9408 = 112 \times x \]

4. **Solve for x**:
To find x, divide both sides by 112:
\[ x = \frac{9408}{112} \]

5. **Perform the division**:
\[ x = 84 \]

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

---