The HCF and LCM of two numbers is 15 and 90 respectively. If one of the two numbers is 30, find the other number

Answer

To find the other number when the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two numbers are given, along with one of the numbers, we can use the formula:

**HCF × LCM = First Number × Second Number**

Given:
- HCF = 15
- LCM = 90
- First Number = 30
- Second Number = ?

Let's denote the second number as \( x \).

### Step 1: Write down the formula
Using the formula, we can express it as:
\[ 15 \times 90 = 30 \times x \]

### Step 2: Calculate the product of HCF and LCM
Now, we calculate \( 15 \times 90 \):
\[ 15 \times 90 = 1350 \]

### Step 3: Set up the equation
Now we have:
\[ 1350 = 30 \times x \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{1350}{30} \]

### Step 5: Perform the division
Now, we divide \( 1350 \) by \( 30 \):
\[ x = 45 \]

### Conclusion
Thus, the other number is \( 45 \).