Greatest Common Divisor of Strings

Problem statement

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.

My solution

 /**
 * @param {string} str1
 * @param {string} str2
 * @return {string}
 */
var gcdOfStrings = function(str1, str2) {
    for (let i = str2.length - 1; i >= 0; i--) {
        const str = str2.slice(0, i + 1);
        if (doesStringRepeat(str, str1) && doesStringRepeat(str, str2)) {
            return str;
        }
        
    }
    
    return "";
    
    function doesStringRepeat(query, searchString) {
        if (query === "") {
            return false;
        }
        let startIndex = searchString.indexOf(query);
        if (startIndex > -1) {
            let appendString = query;
            // console.log(appendString);
            while (appendString.length <= searchString.length) {
                // console.log(appendString)
                if (appendString === searchString) {
                    return true;
                }
                appendString += query;
            }
        }
        return false;
    }
};