Problem:

For two strings s and t, we say "t divides s" if and only if s = t + ... + t (i.e., t is concatenated with itself one or more times).

Given two strings str1 and str2, return the largest string x such that x divides both str1 and str2.

Example 1:

Input: str1 = "ABCABC", str2 = "ABC"
Output: "ABC"

Example 2:

Input: str1 = "ABABAB", str2 = "ABAB"
Output: "AB"

Example 3:

Input: str1 = "LEET", str2 = "CODE"
Output: ""

Constraints:

• 1 <= str1.length, str2.length <= 1000

• str1 and str2 consist of English uppercase letters.

Solution:

Language Used: Java

class Solution 
{
    public boolean valid(String str1, String str2, int k) 
    {
        int len1 = str1.length(), len2 = str2.length();

        if (len1 % k > 0 || len2 % k > 0) 
        {
            return false;
        } 
        else 
        {
            String base = str1.substring(0, k);
            return str1.replace(base, "").isEmpty() && str2.replace(base, "").isEmpty();
        }
    }


    public String gcdOfStrings(String str1, String str2) 
    {
        int len1 = str1.length(), len2 = str2.length();

        for (int i = Math.min(len1, len2); i >= 1; --i) {
            if (valid(str1, str2, i)) {
                return str1.substring(0, i);
            }
        }
        return "";
    }
}