Round #566

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

To find the least common multiple (LCM) of 4, 6, and 9, we need to first find the prime factorization of each number: * 4 = 2^2 * 6 = 2 * 3 * 9 = 3^2 Then, we take the highest power of each prime factor that appears in any of the numbers: * 2 appears with the highest power of 2 in the number 4 (2^2) * 3 appears with the highest power of 2 in the number 9 (3^2) So, the LCM is the product of these highest powers: LCM(4, 6, 9) = 2^2 * 3^2 = 4 * 9 = 36 Therefore, the least common multiple of 4, 6, and 9 is 36. Here is a simple C# code snippet that calculates the LCM of three numbers: ```csharp using System; public class Program { public static void Main() { Console.WriteLine("The LCM of 4, 6, and 9 is: " + FindLCM(4, 6, 9)); } public static int FindLCM(int num1, int num2, int num3) { int lcm = FindLCM(num1, num2); return FindLCM(lcm, num3); } public static int FindLCM(int num1, int num2) { return (num1 * num2) / FindGCD(num1, num2); } public static int FindGCD(int num1, int num2) { while (num2 != 0) { int temp = num2; num2 = num1 % num2; num1 = temp; } return num1; } } ``` This code first calculates the greatest common divisor (GCD) of two numbers using the Euclidean algorithm, then uses the formula `lcm(a, b) = |a*b| / gcd(a, b)` to find the LCM. The `FindLCM` function is overloaded to handle three numbers by first finding the LCM of the first two numbers, then finding the LCM of the result and the third number.

```csharp using System; public class Program { public static int Gcd(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } public static int Lcm(int a, int b) { return Math.Abs(a * b) / Gcd(a, b); } public static int FindLcm(int[] numbers) { int lcm = numbers[0]; for (int i = 1; i < numbers.Length; i++) { lcm = Lcm(lcm, numbers[i]); } return lcm; } public static void Main() { int[] numbers = { 4, 6, 9 }; Console.WriteLine(FindLcm(numbers)); } } ```