Question

I have a code here written in C# that finds the smallest multiple by all numbers from 1 to 20. However, I find it very inefficient since the execution took awhile before producing the correct answer. I would like to know what are the different ways that I can do to improve the code. Thank You.

        public static void SmallestMultiple()
    {
        const ushort ARRAY_SIZE = 21;
        ushort[] array = new ushort[ARRAY_SIZE];
        ushort check = 0;
        for (uint value = 1; value < uint.MaxValue; value++)
        {
            for (ushort j = 1; j < ARRAY_SIZE; j++)
            {
                array[j] = j;
                if (value % array[j] == 0)
                {   
                    check++;
                }
            }
            if (check == 20)
            {
                Console.WriteLine("The value is {0}", value);
            }
            else
            {
                check = 0;
            }
        }
    }

Answer 1

    static void Main(string[] args)
    {
        int[] nums = Enumerable.Range(1, 20).ToArray();
        int lcm = 1;

        for (int i = 0; i < nums.Length; i++)
        {
            lcm = LCM(lcm, nums[i]);
        }
        Console.WriteLine("LCM = {0}", lcm);
    }

    public static int LCM(int value1, int value2)
    {
        int a = Math.Abs(value1);
        int b = Math.Abs(value2);

        // perform division first to avoid potential overflow
        a = checked((a / GCD(a, b)));
        return checked((a * b));
    }

    public static int GCD(int value1, int value2)
    {
        int gcd = 1;     // Greates Common Divisor

        // throw exception if any value=0
        if (value1 == 0 || value2 == 0)
        {
            throw new ArgumentOutOfRangeException();
        }

        // assign absolute values to local vars
        int a = Math.Abs(value1);            // local var1
        int b = Math.Abs(value2);            // local var2

        // if numbers are equal return the first
        if (a == b) { return a; }
            // if var "b" is GCD return "b"
        if (a > b && a % b == 0) { return b; }
            // if var "a" is GCD return "a"
        if (b > a && b % a == 0) { return a; }

        // Euclid algorithm to find GCD (a,b):
        // estimated maximum iterations: 
        // 5* (number of dec digits in smallest number)
        while (b != 0)
        {
            gcd = b;
            b = a % b;
            a = gcd;
        }
        return gcd;
    }
}

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Source : Fast Integer Algorithms: Greatest Common Divisor and Least Common Multiple, .NET solution