How many integers are there from 27000 to 106780 inclusive? Find one multiple of 1323 in this range.

To find the number of integers from 27000 to 106780 (inclusive), we use the formula: Last number - First number + 1.

$$\text{Number of integers} = 106780 - 27000 + 1$$ $$\text{Number of integers} = 79780 + 1$$ $$\text{Number of integers} = 79781$$

The number of integers is $\boxed{\text{79781}}$.

The question asks for one multiple of 1323 within the range of numbers from 27000 to 106780.
First, find the smallest multiple of 1323 that is greater than or equal to 27000.

$$\frac{27000}{1323} \approx 20.408$$

The next integer is 21. So, the first multiple of 1323 in the range is $21 \times 1323$.

$$21 \times 1323 = 27783$$

Since 27783 is between 27000 and 106780, it is a valid answer.
One multiple of 132