Length of longest common subsequence in C#

LongestCommonSubsequence.cs

private static int Max(int int1, int int2)
{
    return int1 > int2 ? int1 : int2;
}

public static int LongestCommonSubsequence(string str1, string str2)
{
    int [,] arr = new int [str1.Length+1, str2.Length+1];
    
    for(int i=0; i<=str2.Length; i++)
    {
        arr[0, i] = 0;
    }
    for (int i = 0; i <= str1.Length; i++)
    {
        arr[i, 0] = 0;
    }

    for (int i = 1; i <= str1.Length; i++)
    {
        for (int j = 1; j <= str2.Length; j++)
        {
            if (str1[i-1] == str2[j-1])
            {
                arr[i, j] = arr[i - 1, j - 1] + 1;
            }
            else
            {
                arr[i, j] = Max(arr[i-1, j], arr[i, j-1]);
            }
        }
    }
    return arr[str1.Length, str2.Length];
}