The LCM and the HCF of two numbers are 240 and 12, respectively. If one of the numbers is 48, then find the other number and arrange the following step in sequential order.
`48xx x=240xx12 implies x=(240xx12)/(48)`
(B) The product of two number =(their LCM) `xx` (their HCF)
(C ) Let the other number be x.
(D) `impliesx=5xx12=60`

Options

A. CABD
B. CBADE
C. BACD
D. CBDA

Answer

To find the other number when given the LCM and HCF of two numbers, we can use the relationship between these values. Here’s how to solve the problem step by step:

### Step-by-Step Solution:

1. **Understand the relationship**:
The relationship between the LCM (Least Common Multiple), HCF (Highest Common Factor), and the two numbers can be expressed as:
\[ \text{LCM} \times \text{HCF} = \text{First Number} \times \text{Second Number} \]

2. **Identify the given values**:
- LCM = 240
- HCF = 12
- First Number = 48
- Let the Second Number be \( x \).

3. **Set up the equation**:
Using the relationship, we can write:
\[ 240 \times 12 = 48 \times x \]

4. **Calculate the left side**:
First, calculate \( 240 \times 12 \):
\[ 240 \times 12 = 2880 \]

5. **Set up the equation with the calculated value**:
Now we have:
\[ 2880 = 48 \times x \]

6. **Solve for \( x \)**:
To find \( x \), divide both sides by 48:
\[ x = \frac{2880}{48} \]

7. **Perform the division**:
Calculate \( \frac{2880}{48} \):
\[ x = 60 \]

8. **Conclusion**:
The other number is \( 60 \).

### Final Answer:
The other number is **60**.

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