Find the LCM of 12,16,20 and 24.
A. 180
B. 220
C. 240
D. 260

Options

A. D
B. A
C. B
D. C

Answer

To find the LCM (Least Common Multiple) of the numbers 12, 16, 20, and 24, we will follow these steps:

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

- **12**:
- 12 = 2 × 6 = 2 × 2 × 3 = \(2^2 × 3^1\)

- **16**:
- 16 = 2 × 8 = 2 × 2 × 4 = 2 × 2 × 2 × 2 = \(2^4\)

- **20**:
- 20 = 2 × 10 = 2 × 2 × 5 = \(2^2 × 5^1\)

- **24**:
- 24 = 2 × 12 = 2 × 2 × 6 = 2 × 2 × 2 × 3 = \(2^3 × 3^1\)

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

- For **2**: The highest power is \(2^4\) (from 16).
- For **3**: The highest power is \(3^1\) (from 12 and 24).
- For **5**: The highest power is \(5^1\) (from 20).

### Step 3: Calculate the LCM
Now, we can calculate the LCM by multiplying the highest powers of all prime factors together:

\[ \text{LCM} = 2^4 × 3^1 × 5^1 \]

Calculating this step-by-step:

1. Calculate \(2^4\):
- \(2^4 = 16\)

2. Calculate \(3^1\):
- \(3^1 = 3\)

3. Calculate \(5^1\):
- \(5^1 = 5\)

Now, multiply these results together:

\[ \text{LCM} = 16 × 3 × 5 \]

4. First, calculate \(16 × 3\):
- \(16 × 3 = 48\)

5. Then, calculate \(48 × 5\):
- \(48 × 5 = 240\)

### Final Answer
Thus, the LCM of 12, 16, 20, and 24 is **240**.

### Options
The correct answer is **C. 240**.

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