The LCM and HCF of two numbers are respectively 2520 and 6. If one number is 120, find the other number.

Answer

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

\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- LCM = 2520
- HCF = 6
- One number (let's call it A) = 120
- Let the other number be B.

2. **Use the Relationship Formula:**
- According to the formula:
\[ \text{LCM} \times \text{HCF} = A \times B \]
- Substitute the known values into the equation:
\[ 2520 \times 6 = 120 \times B \]

3. **Calculate the Left Side:**
- First, calculate \(2520 \times 6\):
\[ 2520 \times 6 = 15120 \]

4. **Set Up the Equation:**
- Now we have:
\[ 15120 = 120 \times B \]

5. **Solve for B:**
- To find B, divide both sides of the equation by 120:
\[ B = \frac{15120}{120} \]

6. **Perform the Division:**
- Now calculate \(15120 \div 120\):
\[ B = 126 \]

7. **Conclusion:**
- The other number is \(B = 126\).

### Final Answer:
The other number is **126**.