The LCM of 12, 15, 18 and 20 would be

Options

A. 175
B. 160
C. 180
D. 220

Answer

To find the LCM (Least Common Multiple) of the numbers 12, 15, 18, and 20, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.

- **12**:
- \(12 = 2^2 \times 3^1\)

- **15**:
- \(15 = 3^1 \times 5^1\)

- **18**:
- \(18 = 2^1 \times 3^2\)

- **20**:
- \(20 = 2^2 \times 5^1\)

### Step 2: Identify the Highest Powers of Each Prime Factor
Next, we identify the highest power of each prime factor present in the factorizations:

- For \(2\): The highest power is \(2^2\) (from 12 and 20).
- For \(3\): The highest power is \(3^2\) (from 18).
- For \(5\): The highest power is \(5^1\) (from 15 and 20).

### Step 3: Multiply the Highest Powers Together
Now, we multiply these highest powers together to get the LCM:

\[ LCM = 2^2 \times 3^2 \times 5^1 \]

Calculating this step-by-step:

1. \(2^2 = 4\)
2. \(3^2 = 9\)
3. \(5^1 = 5\)

Now, multiply these results:

\[ LCM = 4 \times 9 \times 5 \]

### Step 4: Calculate the Product
Calculating the product step-by-step:

1. First, calculate \(4 \times 9 = 36\).
2. Then, multiply \(36 \times 5 = 180\).

Thus, the LCM of 12, 15, 18, and 20 is **180**.

### Final Answer
The LCM of 12, 15, 18, and 20 is **180**.

---