/// <summary>
/// Returns an array of Factors for a series from 2..maxDivisor.
/// </summary>
/// <param name="maxDivisor"></param>
/// <returns></returns>
private PrimeFactors[] GetPrimeFactorsForSeries(int maxDivisor)
{
var primeFactors = new PrimeFactors[maxDivisor - 1];
for (int divisor = 2; divisor <= maxDivisor; divisor++)
{
primeFactors[divisor - 2] = new PrimeFactors(divisor);
}
return primeFactors;
}
/// <summary>
/// This algorithm uses factorial math to speed up the processing.
/// </summary>
/// <param name="maxDivisor"></param>
/// <returns></returns>
/// <remarks>Relies on the fact that common prime factors can be removed to determine
/// LCM (lowest common multiples) of two numbers.</remarks>
public long GetSmallestPositiveNumberEvenlyDivisibleBySeries(int maxDivisor)
{
var primeFactors = GetPrimeFactorsForSeries(maxDivisor);
var divisibleFactors = new PrimeFactors();
for (int i = 0; i < primeFactors.Length; i++)
{
// Calculate LCM
divisibleFactors.AddFactors(
primeFactors[i].RemoveFactors(divisibleFactors));
}
return divisibleFactors.Product;
}
public PrimeFactors RemoveFactors(PrimeFactors factorsToRemove)
{
foreach (long factorToRemove in factorsToRemove.Factors)
MyFactors.Remove(factorToRemove);
return this;
}
public PrimeFactors AddFactors(PrimeFactors factorsToAdd)
{
MyFactors.AddRange(factorsToAdd.Factors);
return this;
}