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

Options

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

Answer

To find the other number given that the LCM of two numbers is 1920, their HCF is 16, and one of the numbers is 128, we can use the relationship between LCM, HCF, and the two numbers.

### Step-by-step Solution:

1. **Understand the relationship**: The relationship between the two numbers (let's call them \( a \) and \( b \)), their LCM (Least Common Multiple), and their HCF (Highest Common Factor) is given by the formula:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]

2. **Substituting known values**: We know:
- LCM = 1920
- HCF = 16
- One of the numbers \( a = 128 \)

Plugging these values into the formula gives:
\[ 1920 \times 16 = 128 \times b \]

3. **Calculate the left side**: First, calculate \( 1920 \times 16 \):
\[ 1920 \times 16 = 30720 \]

4. **Set up the equation**: Now we have:
\[ 30720 = 128 \times b \]

5. **Solve for \( b \)**: To find \( b \), divide both sides by 128:
\[ b = \frac{30720}{128} \]

6. **Perform the division**: Now, calculate \( \frac{30720}{128} \):
\[ b = 240 \]

Thus, the other number is **240**.

### Final Answer:
The other number is **240**.