To solve this problem, we need to determine the greatest common divisor (GCD) of the two numbers, 120 and 150. The GCD will represent the maximum number of identical assortment boxes that can be made using all the cookies with no leftovers.

Steps:

1. Find the GCD of 120 and 150.

   • Prime factorization of 120:
     $120 = 2^3 \times 3 \times 5$
   • Prime factorization of 150:
     $150 = 2 \times 3 \times 5^2$
   • Common factors: $2 \times 3 \times 5 = 30$

2. The GCD of 120 and 150 is 30.

3. Divide each type of cookie by the GCD to determine how many cookies will go into each box:

   • $120 \div 30 = 4$ chocolate chip cookies per box.
   • $150 \div 30 = 5$ oatmeal raisin cookies per box.

4. The maximum number of assortment boxes is 30, with each box containing 4 chocolate chip cookies and 5 oatmeal raisin cookies.

Let me know if you'd like further clarification or have any questions!

Expanding Questions:

1. What is the method to find the least common multiple (LCM) of two numbers?
2. How would the problem change if the number of cookies baked each day were different?
3. What other real-world problems can be solved using GCD?
4. How could this method be extended to three or more types of cookies?
5. Can we automate finding the GCD using a mathematical formula or tool?

Tip: To find the GCD quickly, use the Euclidean algorithm, which involves repeated division and remainders.