Today, I solved the second problem of the LeetCode 75 series. I'd like to share how I approached this problem.

Problem Statement:
You are given two strings, str1 and str2. Return the largest string x such that x divides both str1 and str2.

Examples:

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

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

Input: str1 = "LEET", str2 = "CODE"
Output: ""
**
My Approach**

I divided my solution into three parts:

Check if a common divisor string exists:
First, I check if a common divisor exists by concatenating str1 + str2 and str2 + str1.

If the two concatenated strings are not equal, it means there is no common divisor, and the function returns an empty string ("").

Find the GCD length:
Next, I find the GCD of the lengths of str1 and str2.

I use a recursive gcd() function. If b !== 0, the function calls itself recursively with two arguments:
gcd(a, b) = gcd(b, a % b)
Once b = 0, the function returns a, which is the GCD length.

Example Calculation:

Initial Call: gcd(6, 3)
Since b = 3 is not 0, it recursively calls gcd(3, 6 % 3) → gcd(3, 0)

Second Call: gcd(3, 0)
Now b = 0, so the function returns 3.

Extract the GCD substring:
Finally, I extract the substring from str1 using the gcdlength.

function gcdOfStrings(str1, str2) {
  // recursive function to calculate the GCD of two numbers
  function gcd(a, b) {
    console.log(a, b);
    return b === 0 ? a : gcd(b, a % b);
  }

  // Step 1: Check if str1 and str2 match or not
  if (str1 + str2 !== str2 + str1) {
    return ""; // No common pattern exists
  }

  // Step 2: Find the GCD of the lengths of str1 and str2
  const len1 = str1.length;
  const len2 = str2.length;
  const gcdLength = gcd(len1, len2);

  // Step 3: The largest divisor substring
  return str1.substring(0, gcdLength);
}

// Example usage:
console.log(gcdOfStrings("ABCABC", "ABC")); // Output: "ABC"
console.log(gcdOfStrings("ABABAB", "ABAB")); // Output: "AB"
console.log(gcdOfStrings("LEET", "CODE")); // Output: ""

If you have better solutions or ideas, feel free to share with me.