If AM and HM between two numbers are 27 and 12 respectively, then their GM is

Options

A. 9
B. 18
C. 24
D. 36

Answer

To solve the problem, we need to find the geometric mean (GM) of two numbers given their arithmetic mean (AM) and harmonic mean (HM). The provided values are:

- AM = 27
- HM = 12

We can use the relationship between AM, HM, and GM, which states:

\[ GM^2 = AM \times HM \]

### Step-by-step solution:

1. **Write down the formula for GM**:
\[ GM^2 = AM \times HM \]

2. **Substitute the values of AM and HM**:
\[ GM^2 = 27 \times 12 \]

3. **Calculate the product of AM and HM**:
\[ GM^2 = 324 \]

4. **Take the square root of both sides to find GM**:
\[ GM = \sqrt{324} \]

5. **Calculate the square root**:
\[ GM = 18 \]

Thus, the geometric mean (GM) of the two numbers is **18**.