Find the LCM of 8, 15, 24 and 72.

Options

A. 350
B. 360
C. 720
D. 735

Answer

To find the LCM (Least Common Multiple) of the numbers 8, 15, 24, and 72, we will follow these steps:

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

- **8**:
- \(8 = 2^3\)

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

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

- **72**:
- \(72 = 2^3 \times 3^2\)

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

- For \(2\): The highest power is \(2^3\) (from 8, 24, and 72).
- For \(3\): The highest power is \(3^2\) (from 72).
- For \(5\): The highest power is \(5^1\) (from 15).

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

\[ \text{LCM} = 2^3 \times 3^2 \times 5^1 \]

Calculating this step-by-step:

1. Calculate \(2^3\):
\[ 2^3 = 8 \]

2. Calculate \(3^2\):
\[ 3^2 = 9 \]

3. Calculate \(5^1\):
\[ 5^1 = 5 \]

4. Now multiply these results together:
\[ 8 \times 9 = 72 \]
\[ 72 \times 5 = 360 \]

Thus, the LCM of 8, 15, 24, and 72 is **360**.

### Final Answer:
The LCM of 8, 15, 24, and 72 is **360**.

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