/// <summary>
/// Calculates the least common multiple of a collection of numbers
/// </summary>
/// <param name="numbers">The numbers to find the LCM of</param>
/// <returns>The factorization of the LCM of <paramref name="numbers"/></returns>
public static Factorization LCM(params long[] numbers)
{
if (numbers == null)
{
throw new ArgumentNullException(nameof(numbers));
}
if (numbers.Length < 1)
{
throw new ArgumentException("At least one number is required for finding the least common multiple!", nameof(numbers));
}
var factorizations = numbers.Select(n => Factorization.Of(n)).ToList();
var allPrimes = new HashSet <long>(factorizations.SelectMany(d => d.Keys));
return(new Factorization(allPrimes.Select(p => (p, factorizations.Max(f => f.GetExponent(p))))));
}
/// <summary>
/// Calculates a binomial coefficient C(n, k)
/// </summary>
/// <param name="n">The number of items to select from</param>
/// <param name="k">The number of items to select</param>
/// <returns>A binomial coefficient C(n, k), ie. the number of ways to choose <paramref name="k"/> items from <paramref name="n"/> distinct ones</returns>
public static Factorization Binomial(int n, int k)
{
return(Factorization.OfFactorial(n) / (Factorization.OfFactorial(k) * Factorization.OfFactorial(n - k)));
}