The LCM of two numbers is 864 and their HCF is 144 . If one of the number is 288 , the other number is

Options

A. 576
B. 1296
C. 432
D. 144

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 relationship is given by the formula:

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

Given:
- LCM = 864
- HCF = 144
- One number (Number 1) = 288

Let's denote the other number as \( x \).

### Step-by-Step Solution:

1. **Write the formula**:
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]
Substituting the known values:
\[ 864 \times 144 = 288 \times x \]

2. **Calculate the left side**:
First, we need to calculate \( 864 \times 144 \):
\[ 864 \times 144 = 124416 \]

3. **Set up the equation**:
Now we have:
\[ 124416 = 288 \times x \]

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

5. **Perform the division**:
Now, calculate \( \frac{124416}{288} \):
\[ x = 432 \]

### Conclusion:
The other number is \( 432 \).