Find the LCM of the numbers given below :
12, 18, 20

Answer

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

### Step 1: Find the Prime Factorization of Each Number
- **12**: The prime factorization of 12 is \(2^2 \times 3^1\).
- **18**: The prime factorization of 18 is \(2^1 \times 3^2\).
- **20**: The prime factorization of 20 is \(2^2 \times 5^1\).

### Step 2: Identify the Highest Power of Each Prime Factor
Now, we will identify the highest power of each prime factor from the factorizations:
- For the prime factor **2**: The highest power is \(2^2\) (from 12 and 20).
- For the prime factor **3**: The highest power is \(3^2\) (from 18).
- For the prime factor **5**: The highest power is \(5^1\) (from 20).

### Step 3: Multiply the Highest Powers Together
Now, we will multiply these highest powers together to find the LCM:
\[ LCM = 2^2 \times 3^2 \times 5^1 \]

Calculating this step-by-step:
- First, calculate \(2^2 = 4\).
- Next, calculate \(3^2 = 9\).
- Then, multiply \(4 \times 9 = 36\).
- Finally, multiply \(36 \times 5 = 180\).

### Final Answer
Thus, the LCM of 12, 18, and 20 is **180**.

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