The HCF and LCM of two numbers are 3 and 2730 respectively. If one of the numbers is 78, find the other number.
A. 107
B. 106
C. 105
D. 103

Options

A. B
B. D
C. A
D. C

Answer

To find the other number when the HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers are given, along with one of the numbers, we can use the relationship:

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

Given:
- HCF = 3
- LCM = 2730
- First Number = 78

We need to find the Second Number.

### Step-by-step Solution:

1. **Use the relationship between HCF, LCM, and the two numbers**:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

2. **Substitute the known values into the equation**:
\[ 3 \times 2730 = 78 \times \text{Second Number} \]

3. **Calculate the left side**:
\[ 3 \times 2730 = 8190 \]

4. **Set up the equation**:
\[ 8190 = 78 \times \text{Second Number} \]

5. **Solve for the Second Number**:
\[ \text{Second Number} = \frac{8190}{78} \]

6. **Perform the division**:
\[ \text{Second Number} = 105 \]

Thus, the other number is **105**.

### Final Answer:
The other number is **105** (Option C).