List multiples of numbers within given ranges and identify common factors.

Here are the solutions to the multiples problems:

1. Write the multiples of 3 between 10 and 30. The multiples of 3 are $3, 6, 9, 12, 15, 18, 21, 24, 27, 30, \dots$. The multiples between 10 and 30 are those greater than 10 and less than 30.

$$\boxed{12, 15, 18, 21, 24, 27}$$

2. Write the multiples of 4 between 15 and 40. The multiples of 4 are $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \dots$. The multiples between 15 and 40 are those greater than 15 and less than 40.

$$\boxed{16, 20, 24, 28, 32, 36}$$

3. Write the multiples of 5 between 20 and 55. The multiples of 5 are $5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, \dots$. The multiples between 20 and 55 are those greater than 20 and less than 55.

$$\boxed{25, 30, 35, 40, 45, 50}$$

4. Write the multiples of 9 between 30 and 90. The multiples of 9 are $9, 18, 27, 36, 45, 54, 63, 72, 81, 90, \dots$. The multiples between 30 and 90 are those greater than 30 and less than 90.

$$\boxed{36, 45, 54, 63, 72, 81}$$

5. 10, 15, 20, 30 are multiples of All these numbers are divisible by 5.

$$\boxed{5}$$

6. 12, 15, 18, 21 are multiples of All these numbers are divisible by 3.

$$\boxed{3}$$

7. 10, 20, 30, 40 are multiples of All these numbers are divisible by 10.

$$\boxed{10}$$

8. 12, 24, 36, 42 are multiples of All these numbers are divisible by 6.

$$\boxed{6}$$