Identify the LCM of the numbers 28, 16 and 12 among the options.

Options

A. 160
B. 330
C. 448
D. 192

Answer

To find the LCM (Least Common Multiple) of the numbers 28, 16, and 12, we will follow these steps:

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

- **28**:
- Divide by 2: \( 28 \div 2 = 14 \)
- Divide by 2 again: \( 14 \div 2 = 7 \)
- 7 is a prime number.
- So, the prime factorization of 28 is \( 2^2 \times 7^1 \).

- **16**:
- Divide by 2: \( 16 \div 2 = 8 \)
- Divide by 2: \( 8 \div 2 = 4 \)
- Divide by 2: \( 4 \div 2 = 2 \)
- Divide by 2: \( 2 \div 2 = 1 \)
- So, the prime factorization of 16 is \( 2^4 \).

- **12**:
- Divide by 2: \( 12 \div 2 = 6 \)
- Divide by 2: \( 6 \div 2 = 3 \)
- 3 is a prime number.
- So, the prime factorization of 12 is \( 2^2 \times 3^1 \).

### Step 2: Identify the Highest Powers
Next, we 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).
- For \( 7 \): The highest power is \( 7^1 \) (from 28).

### Step 3: Calculate the LCM
Now, we multiply these highest powers together to find the LCM:

\[ \text{LCM} = 2^4 \times 3^1 \times 7^1 \]

Calculating this step-by-step:

1. \( 2^4 = 16 \)
2. \( 3^1 = 3 \)
3. \( 7^1 = 7 \)

Now, multiply these results:

\[ 16 \times 3 = 48 \]
\[ 48 \times 7 = 336 \]

### Conclusion
Thus, the LCM of 28, 16, and 12 is **336**.

### Options Check
Among the given options (160, 330, 448, 192), none of them match the calculated LCM of 336.

### Final Answer
The correct answer is **336**, which is not listed among the options.

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