The LCM 16,24,36,52 and 54 is ?

Options

A. 5618
B. 5216
C. 432
D. 5616

Answer

To find the LCM (Least Common Multiple) of the numbers 16, 24, 36, 52, and 54, we can follow these steps:

### Step 1: Prime Factorization
First, we need to factor each number into its prime factors.

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

- **24**:
- \(24 = 2^3 \times 3^1\)

- **36**:
- \(36 = 2^2 \times 3^2\)

- **52**:
- \(52 = 2^2 \times 13^1\)

- **54**:
- \(54 = 2^1 \times 3^3\)

### Step 2: Identify the Highest Powers
Next, we identify the highest power of each prime number that appears in the factorizations:

- For \(2\): The highest power is \(2^4\) (from 16).
- For \(3\): The highest power is \(3^3\) (from 54).
- For \(13\): The highest power is \(13^1\) (from 52).

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

\[ \text{LCM} = 2^4 \times 3^3 \times 13^1 \]

Calculating this step by step:

- First, calculate \(2^4\):
\[ 2^4 = 16 \]

- Next, calculate \(3^3\):
\[ 3^3 = 27 \]

- Now, multiply \(16\) and \(27\):
\[ 16 \times 27 = 432 \]

- Finally, multiply \(432\) by \(13\):
\[ 432 \times 13 = 5616 \]

### Final Answer
Thus, the LCM of 16, 24, 36, 52, and 54 is **5616**.

---