HCF and LCM of two numbers are 144 and 864 . If one number is 288 find 2nd number.

Answer

To find the second number when the HCF (also known as GCD) and LCM of two numbers are given, we can use the relationship between these values. The formula we will use is:

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

### Step-by-Step Solution:

1. **Identify the Given Values**:
- HCF = 144
- LCM = 864
- First number (N1) = 288
- Second number (N2) = ?

2. **Use the Relationship Formula**:
We know from the formula that:
\[ \text{HCF} \times \text{LCM} = N1 \times N2 \]

3. **Substitute the Known Values**:
Substitute the values into the equation:
\[ 144 \times 864 = 288 \times N2 \]

4. **Calculate the Left Side**:
Calculate \(144 \times 864\):
\[ 144 \times 864 = 124416 \]

5. **Set Up the Equation**:
Now we have:
\[ 124416 = 288 \times N2 \]

6. **Solve for N2**:
To find \(N2\), divide both sides by 288:
\[ N2 = \frac{124416}{288} \]

7. **Calculate N2**:
Performing the division:
\[ N2 = 432 \]

8. **Conclusion**:
The second number is \(432\).

### Final Answer:
The second number is **432**.