The least number divisible by each of the numbers 15, 20, 24, 32 and 36 is

Options

A. 1660
B. 2880
C. 1440
D. none of these

Answer

To find the least number divisible by each of the numbers 15, 20, 24, 32, and 36, we will calculate the Least Common Multiple (LCM) of these numbers. Here’s a step-by-step solution:

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

- **15**: \(3 \times 5\)
- **20**: \(2^2 \times 5\)
- **24**: \(2^3 \times 3\)
- **32**: \(2^5\)
- **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 factor from 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 this step-by-step:

1. Calculate \(2^5 = 32\)
2. Calculate \(3^2 = 9\)
3. Calculate \(5^1 = 5\)

Now multiply these results together:

\[ 32 \times 9 = 288 \]
\[ 288 \times 5 = 1440 \]

### Final Answer
The least number divisible by each of the numbers 15, 20, 24, 32, and 36 is **1440**.

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