The LCM and HCF of two numbers are 4284 and 32 , respectively .If one of the numbers is 762 , then the second number is :

Options

A. 102
B. 64
C. 204
D. 92

Answer

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

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

Given:
- LCM = 4284
- HCF = 32
- First Number = 762

Let the second number be \( x \).

### Step 1: Write the equation using the formula
Using the formula, we can write:

\[ 32 \times 4284 = 762 \times x \]

### Step 2: Calculate the left side of the equation
Now, we need to calculate \( 32 \times 4284 \):

\[ 32 \times 4284 = 102048 \]

### Step 3: Set up the equation
Now, we can set up the equation:

\[ 102048 = 762 \times x \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:

\[ x = \frac{102048}{762} \]

### Step 5: Perform the division
Now, we perform the division:

\[ x = 134.0 \]

### Step 6: Conclusion
Thus, the second number is:

\[ x = 134 \]