Python Code with Simple Logic || Using Python Dictionaries for efficient look-up during iteration 
Code
# Code
```python3 []
class Solution:
    def maxDivScore(self, nums: List[int], divisors: List[int]) -> int:
        score = {}
        for i in range(len(divisors)):
            count = 0
            for j in range(len(nums)):
                if nums[j]%divisors[i]==0:
                    count+=1
            if i==0:
                score[divisors[i]] = count
            elif i>0 and count>=max(score.values()):
                score[divisors[i]] = count
        max_score = max(score.values())
        for i in list(score.keys()):
            if score[i]<max_score:
                del score[i]
        return min(score.keys())
```
['Python3']