To find the greatest number of identical refreshment tables that Kira can stock without having any sodas left over, we need to determine the greatest common divisor (GCD) of the 12 cans of regular soda and 18 cans of diet soda.

First, let's find the factors of each number:

• The factors of 12 are: 1, 2, 3, 4, 6, 12.
• The factors of 18 are: 1, 2, 3, 6, 9, 18.

The common factors of 12 and 18 are 1, 2, 3, and 6. The greatest common divisor (GCD) is 6.

Therefore, the greatest number of refreshment tables Kira can stock is 6.

This means:

• Each table will have $\frac{12}{6} = 2$ cans of regular soda.
• Each table will have $\frac{18}{6} = 3$ cans of diet soda.

Would you like any further details or have any questions? Here are five related questions to expand on this topic:

1. What if Kira had 24 cans of regular soda and 30 cans of diet soda? What would be the greatest number of tables she could stock?
2. How do you determine the greatest common divisor (GCD) for larger numbers?
3. What is the significance of the GCD in this kind of problem?
4. Can you think of other scenarios where finding the GCD would be useful?
5. How would the solution change if Kira had an odd number of cans for each type of soda?

Tip: Understanding the concept of GCD helps simplify many distribution and partitioning problems, making them easier to solve.