Find the least number divisible by 15, 20, 24, 32 and 36.

Answer

To find the least number that is divisible by 15, 20, 24, 32, and 36, we need to calculate the Least Common Multiple (LCM) of these numbers. Here’s how we can do it step by step:

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

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

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

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

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

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

### 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 \( 2^5 \) (from 32).
- For **3**: The highest power is \( 3^2 \) (from 36).
- For **5**: The highest power is \( 5^1 \) (from 15 and 20).

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

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

Calculating each part:

- \( 2^5 = 32 \)
- \( 3^2 = 9 \)
- \( 5^1 = 5 \)

Now, multiply these results together:

\[ \text{LCM} = 32 \times 9 \times 5 \]

Calculating step by step:

1. \( 32 \times 9 = 288 \)
2. \( 288 \times 5 = 1440 \)

### Final Answer
Thus, the least number that is divisible by 15, 20, 24, 32, and 36 is **1440**.

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