According to above problem find the largest possible number of 4 digits which is exactly divisible by 32, 36 and 40.

Answer

To find the largest possible 4-digit number that is exactly divisible by 32, 36, and 40, we will follow these steps:

### Step 1: Find the LCM of 32, 36, and 40
To find the LCM, we first need to perform the prime factorization of each number:

- **32**:
\[ 32 = 2^5 \]

- **36**:
\[ 36 = 2^2 \times 3^2 \]

- **40**:
\[ 40 = 2^3 \times 5^1 \]

Now, we take the highest power of each prime factor:

- 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 40).

Thus, the LCM is:
\[ LCM = 2^5 \times 3^2 \times 5^1 \]

### Step 2: Calculate the LCM
Now, we calculate the LCM:
\[ LCM = 32 \times 9 \times 5 \]

Calculating step-by-step:
- First, calculate \(32 \times 9 = 288\).
- Then, calculate \(288 \times 5 = 1440\).

So, the LCM of 32, 36, and 40 is:
\[ LCM = 1440 \]

### Step 3: Find the largest 4-digit number divisible by 1440
The largest 4-digit number is 9999. To find the largest multiple of 1440 that is less than or equal to 9999, we divide 9999 by 1440 and take the integer part of the result:
\[ \frac{9999}{1440} \approx 6.949 \]
Taking the integer part, we have \(6\).

### Step 4: Multiply to find the largest 4-digit number
Now, we multiply 1440 by 6:
\[ 1440 \times 6 = 8640 \]

### Conclusion
The largest possible 4-digit number that is exactly divisible by 32, 36, and 40 is:
\[ \boxed{8640} \]

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