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 given the LCM, HCF, and one of the numbers, we can use the relationship between these values. Let's break down the solution step by step.

### Step 1: Understand the relationship between LCM, HCF, and the two numbers
The relationship states that:
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]
Where:
- LCM = 864
- HCF = 144
- Number 1 = 288
- Number 2 = ?

### Step 2: Substitute the known values into the equation
We can substitute the known values into the equation:
\[ 864 \times 144 = 288 \times \text{Number 2} \]

### Step 3: Calculate the left-hand side
Now, we calculate the left-hand side:
\[ 864 \times 144 = 124416 \]

### Step 4: Set up the equation to find Number 2
Now we have:
\[ 124416 = 288 \times \text{Number 2} \]

### Step 5: Solve for Number 2
To find Number 2, we can rearrange the equation:
\[ \text{Number 2} = \frac{124416}{288} \]

### Step 6: Perform the division
Now we perform the division:
\[ \text{Number 2} = 432 \]

### Conclusion
Thus, the other number is **432**.

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