The HCF of two numbers is `27` and their LCM is `162`. if one of numbers is `81`, find the other.

Answer

To find the other number when the HCF and LCM are given, we can use the relationship between them. The product of the two numbers is equal to the product of their HCF and LCM.

### Step-by-Step Solution:

1. **Identify the given values:**
- HCF (Highest Common Factor) = 27
- LCM (Lowest Common Multiple) = 162
- One of the numbers (let's call it \( a \)) = 81
- The other number (let's call it \( b \)) = ?

2. **Use the relationship between HCF, LCM, and the two numbers:**
\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]
Therefore,
\[ a \times b = \text{HCF} \times \text{LCM} \]

3. **Substitute the known values into the equation:**
\[ 81 \times b = 27 \times 162 \]

4. **Calculate the right side of the equation:**
\[ 27 \times 162 = 4374 \]
So, we have:
\[ 81 \times b = 4374 \]

5. **Solve for \( b \):**
\[ b = \frac{4374}{81} \]

6. **Perform the division:**
\[ b = 54 \]

7. **Conclusion:**
The other number is \( b = 54 \).