What will be the LCM of 15, 24, 32 and 45?

Answer

To find the LCM (Lowest Common Multiple) of the numbers 15, 24, 32, and 45, we can follow these steps:

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

- **15**: The prime factors are \(3 \times 5\).
- **24**: The prime factors are \(2^3 \times 3\) (since \(24 = 2 \times 2 \times 2 \times 3\)).
- **32**: The prime factors are \(2^5\) (since \(32 = 2 \times 2 \times 2 \times 2 \times 2\)).
- **45**: The prime factors are \(3^2 \times 5\) (since \(45 = 3 \times 3 \times 5\)).

### Step 2: List the Highest Powers of Each Prime Factor
Next, we will list all the prime factors and take the highest power of each:

- For **2**: The highest power is \(2^5\) (from 32).
- For **3**: The highest power is \(3^2\) (from 45).
- For **5**: The highest power is \(5^1\) (from both 15 and 45).

### Step 3: Calculate the LCM
Now, we 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 Result
Thus, the LCM of 15, 24, 32, and 45 is **1440**.

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