The LCM of 20, 24 , 30 and 32 would be

Options

A. 398
B. 410
C. 450
D. 480

Answer

To find the LCM (Least Common Multiple) of the numbers 20, 24, 30, and 32, we will follow these steps:

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

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

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

- **30**:
- \(30 = 2^1 \times 3^1 \times 5^1\)

- **32**:
- \(32 = 2^5\)

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

- For \(2\): The highest power is \(2^5\) (from 32).
- For \(3\): The highest power is \(3^1\) (from 24 and 30).
- For \(5\): The highest power is \(5^1\) (from 20 and 30).

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

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

Calculating this step-by-step:

1. Calculate \(2^5\):
\[ 2^5 = 32 \]

2. Multiply by \(3^1\):
\[ 32 \times 3 = 96 \]

3. Multiply by \(5^1\):
\[ 96 \times 5 = 480 \]

Thus, the LCM of 20, 24, 30, and 32 is **480**.

### Final Answer:
The LCM of 20, 24, 30, and 32 is **480**.

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