The LCM and HCF of two natural number is 12 and 2 respectively. If one numbers is 4 . Find the other numbers .

Answer

To find the other number when the LCM and HCF of two natural numbers are given, we can use the relationship between LCM, HCF, and the two numbers. Here's how to solve the problem step by step:

### Step-by-Step Solution:

1. **Identify the given values:**
- LCM (Least Common Multiple) = 12
- HCF (Highest Common Factor) = 2
- One number (let's call it n1) = 4
- The other number (let's call it n2) is what we need to find.

2. **Use the relationship between LCM, HCF, and the two numbers:**
The formula that relates these values is:
\[ \text{LCM} \times \text{HCF} = n1 \times n2 \]

3. **Substitute the known values into the formula:**
\[ 12 \times 2 = 4 \times n2 \]

4. **Calculate the left side:**
\[ 24 = 4 \times n2 \]

5. **Solve for n2:**
To find n2, divide both sides of the equation by 4:
\[ n2 = \frac{24}{4} \]
\[ n2 = 6 \]

6. **Conclusion:**
The other number is 6.

### Final Answer:
The other number is **6**.