The L.C.M. of two numbers is 2310 and their H.C.F is 30. If one number is 210, the other number is-

Options

A. 330
B. 1470
C. 2100
D. 16170

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 that relates the two numbers (let's call them A and B), their LCM (Least Common Multiple), and their HCF (Highest Common Factor) is:

\[ A \times B = \text{LCM}(A, B) \times \text{HCF}(A, B) \]

Given:
- LCM = 2310
- HCF = 30
- One number (A) = 210

We need to find the other number (B).

### Step-by-Step Solution:

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

2. **Substitute the known values**:
\[ 210 \times B = 2310 \times 30 \]

3. **Calculate the right-hand side**:
- First, calculate \( 2310 \times 30 \):
\[ 2310 \times 30 = 69300 \]

4. **Now, we have**:
\[ 210 \times B = 69300 \]

5. **Solve for B**:
\[ B = \frac{69300}{210} \]

6. **Perform the division**:
- Simplifying \( \frac{69300}{210} \):
\[ B = 330 \]

### Conclusion:
The other number is **330**.