The LCM and HCF of two numbers are 3456 and 48 respectively. If first no is 432 then find the 2nd number.

Options

A. 384
B. 192
C. 108
D. 96

Answer

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

\[ \text{LCM} \times \text{HCF} = \text{First Number} \times \text{Second Number} \]

### Step-by-Step Solution:

**Step 1: Write down the given values.**
- LCM = 3456
- HCF = 48
- First Number = 432
- Let the Second Number be \( x \).

**Step 2: Substitute the values into the formula.**
Using the formula mentioned above, we have:

\[ 3456 \times 48 = 432 \times x \]

**Step 3: Calculate the left-hand side.**
First, calculate \( 3456 \times 48 \):

\[ 3456 \times 48 = 165888 \]

**Step 4: Set up the equation.**
Now, we can set up the equation:

\[ 165888 = 432 \times x \]

**Step 5: Solve for \( x \).**
To find \( x \), divide both sides by 432:

\[ x = \frac{165888}{432} \]

**Step 6: Perform the division.**
Now, calculate \( \frac{165888}{432} \):

\[ x = 384 \]

### Conclusion:
The second number is \( 384 \).

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