The GCD of two whole numbers is 6 and their LCM is 60. If one of the numbers is 20, then other number would be :

Options

A. 25
B. 13
C. 16
D. 18

Answer

To find the other number when one number is given, we can use the relationship between the GCD (Greatest Common Divisor), LCM (Least Common Multiple), and the two numbers. The formula we will use is:

\[ \text{GCD}(a, b) \times \text{LCM}(a, b) = a \times b \]

Where:
- \( a \) and \( b \) are the two numbers,
- GCD is given as 6,
- LCM is given as 60,
- One of the numbers \( a \) is given as 20.

### Step-by-step Solution:

1. **Identify the known values**:
- GCD = 6
- LCM = 60
- One number \( a = 20 \)
- We need to find the other number \( b \).

2. **Use the formula**:
\[ \text{GCD}(a, b) \times \text{LCM}(a, b) = a \times b \]
Substituting the known values into the formula:
\[ 6 \times 60 = 20 \times b \]

3. **Calculate the left side**:
\[ 360 = 20 \times b \]

4. **Solve for \( b \)**:
To find \( b \), divide both sides by 20:
\[ b = \frac{360}{20} \]

5. **Perform the division**:
\[ b = 18 \]

### Conclusion:
The other number is \( b = 18 \).