Find the least possible number which can be divided by 32, 36 and 40.

Answer

To find the least possible number that can be divided by 32, 36, and 40, we need to calculate the Least Common Multiple (LCM) of these three numbers. Here’s how to do it step by step:

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

- **For 32**:
- \(32 = 2^5\) (since \(32 = 2 \times 2 \times 2 \times 2 \times 2\))

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

- **For 40**:
- \(40 = 2^3 \times 5^1\) (since \(40 = 2 \times 2 \times 2 \times 5\))

### Step 2: Identify the Highest Powers
Next, we identify the highest power of each prime factor from the factorizations:

- For the prime factor **2**:
- The highest power is \(2^5\) (from 32).

- For the prime factor **3**:
- The highest power is \(3^2\) (from 36).

- For the prime factor **5**:
- The highest power is \(5^1\) (from 40).

### Step 3: Calculate the LCM
Now, we can calculate the LCM by multiplying these highest powers together:

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

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:

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

### Step 4: Perform the Multiplication
1. First, multiply \(32 \times 9\):
\[ 32 \times 9 = 288 \]

2. Next, multiply the result by 5:
\[ 288 \times 5 = 1440 \]

### Conclusion
Thus, the least possible number which can be divided by 32, 36, and 40 is **1440**.