The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.

Options

A. 204
B. 240
C. 260
D. 320

Answer

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

\[ \text{LCM} \times \text{HCF} = n_1 \times n_2 \]

Where:
- LCM is the least common multiple,
- HCF is the highest common factor,
- \( n_1 \) and \( n_2 \) are the two numbers.

Given:
- LCM = 1920
- HCF = 16
- \( n_1 = 128 \)
- \( n_2 = x \) (the number we need to find)

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

\[ 1920 \times 16 = 128 \times x \]

### Step 2: Calculate the left side of the equation
Now, we calculate the left side:

\[ 1920 \times 16 = 30720 \]

### Step 3: Set up the equation
Now our equation looks like this:

\[ 30720 = 128 \times x \]

### Step 4: Solve for \( x \)
To find \( x \), we divide both sides by 128:

\[ x = \frac{30720}{128} \]

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

\[ x = 240 \]

### Conclusion
Thus, the other number is \( 240 \).