Round #651

What is the least common multiple of 4, 6, and 9?

To find the least common multiple (LCM) of 4, 6, and 9 in C#, you can use the following code: ```csharp using System; class Program { static void Main() { int num1 = 4; int num2 = 6; int num3 = 9; int lcm = LCM(num1, LCM(num2, num3)); Console.WriteLine("The least common multiple of " + num1 + ", " + num2 + ", and " + num3 + " is: " + lcm); } static int GCD(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } static int LCM(int a, int b) { return (a / GCD(a, b)) * b; } } ``` This code defines two methods: `GCD` (greatest common divisor) and `LCM` (least common multiple). The `LCM` method uses the formula `LCM(a, b) = (a / GCD(a, b)) * b`. In the `Main` method, it calculates the LCM of 4, 6, and 9 by first finding the LCM of 6 and 9, then finding the LCM of that result with 4. The final LCM is printed to the console.

To find the least common multiple (LCM) of 4, 6, and 9, we can use a straightforward approach by calculating the LCM of pairs of numbers iteratively. The LCM of two numbers \(a\) and \(b\) can be calculated using their greatest common divisor (GCD): \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \] We will use the `System.Numerics` namespace to get the GCD function. Here is the complete code in C#: ```csharp using System; using System.Numerics; class Program { static void Main() { int[] numbers = { 4, 6, 9 }; int lcm = CalculateLCM(numbers); Console.WriteLine($"The least common multiple of {string.Join(", ", numbers)} is {lcm}"); } static int CalculateLCM(int[] numbers) { if (numbers == null || numbers.Length == 0) throw new ArgumentException("Array must contain at least one number."); int result = numbers[0]; for (int i = 1; i < numbers.Length; i++) { result = LCM(result, numbers[i]); } return result; } static int LCM(int a, int b) { if (a == 0 || b == 0) return 0; return Math.Abs(a * b) / GCD(a, b); } static int GCD(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } } ``` ### Explanation: 1. **Main Method**: - We define an array of integers containing the numbers for which we want to find the LCM. - We call the `CalculateLCM` method and print the result. 2. **CalculateLCM Method**: - This method takes an array of integers as input. - It initializes the result with the first number in the array. - It iterates through the rest of the numbers, updating the result by calculating the LCM of the current result and the next number using the `LCM` method. 3. **LCM Method**: - This method calculates the least common multiple of two integers. - It uses the formula \(\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}\). - If either `a` or `b` is zero, it returns 0 because the LCM of any number with zero is zero. 4. **GCD Method**: - This method calculates the greatest common divisor of two integers using the Euclidean algorithm. - The algorithm repeatedly replaces the larger number by its remainder when divided by the smaller number until one of the numbers becomes zero. The non-zero number at this point is the GCD. This code is efficient and follows best practices in C#, including proper error handling and clear method separation for readability.