The LCM of two numbers is 2376 while their HCF is 33. If one of the numbers is 297, then the other number is?

Options

A. 216
B. 264
C. 642
D. 792

Answer

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

\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- LCM = 2376
- HCF = 33
- One number (let's call it \( a \)) = 297
- The other number (let's call it \( b \)) = ?

2. **Use the Formula:**
According to the formula:
\[ \text{HCF} \times \text{LCM} = a \times b \]
Plugging in the known values:
\[ 33 \times 2376 = 297 \times b \]

3. **Calculate the Left Side:**
First, we need to calculate \( 33 \times 2376 \):
\[ 33 \times 2376 = 78528 \]

4. **Set Up the Equation:**
Now we have:
\[ 78528 = 297 \times b \]

5. **Solve for \( b \):**
To find \( b \), divide both sides by 297:
\[ b = \frac{78528}{297} \]

6. **Perform the Division:**
Now calculate \( \frac{78528}{297} \):
\[ b = 264 \]

7. **Conclusion:**
The other number is \( 264 \).

### Final Answer:
The other number is **264**.