JoinPointExample.cs

public class JoinPointExample
{
    private const int Max = 10000000;

    private static int SumDigits(int num)
    {
        int sum = 0;

        while (num > 0)
        {
            sum += num % 10;
            num /= 10;
        }

        return sum;
    }

    public static int ComputeJoinPoint(int sequence1, int sequence2)
    {
        while (sequence1 != sequence2)
        {
            if (sequence1 >= Max || sequence2 >= Max)
                return -1;
            while (sequence1 < sequence2)
                sequence1 += SumDigits(sequence1);
            while (sequence2 < sequence1)
                sequence2 += SumDigits(sequence2);
        }
        return sequence1;
    }

    public static void Test(int sequence1 = 471, int sequence2 = 480, int expectedResult = 519)
    {
        var result = ComputeJoinPoint(sequence1, sequence2);
        System.Diagnostics.Debug.Assert(result == expectedResult);
        Console.WriteLine($"The join point of {sequence1} and {sequence2} is: {result}");
    }
}