The LCM of two numbers is 1820 and their HCF is 26. If one number is 130 then the other number is:

Options

A. 70
B. 1690
C. 364
D. 1264

Answer

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

\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]

Given:
- LCM = 1820
- HCF = 26
- One number (Number 1) = 130
- The other number (Number 2) = X (which we need to find)

### Step-by-Step Solution:

1. **Write the relationship formula:**
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]
Substituting the known values:
\[ 1820 \times 26 = 130 \times X \]

2. **Calculate the left side of the equation:**
\[ 1820 \times 26 = 47320 \]
Now, we have:
\[ 47320 = 130 \times X \]

3. **Rearranging the equation to solve for X:**
\[ X = \frac{47320}{130} \]

4. **Perform the division:**
\[ X = 364 \]

5. **Conclusion:**
The other number is 364.

### Final Answer:
The other number is **364**.