Final answer:
The largest number Amelia could be thinking of is 3.
Step-by-step explanation:
To find the largest number Amelia could be thinking of, we need to find the common factors of 18 and 12 that are odd. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors of both numbers are 1, 2, 3, and 6. Among these, the largest odd number is 3. Therefore, the largest number Amelia could be thinking of is 3.