#include <map>
#include <vector>
#include <cmath>

const int NUMBER = 20;

bool isPrime(int number);
int getNextPrime(int number);
std::map<int, int> getPrimeFactors(int number);
int getRangeLeastCommonMultiple(int maxNumber);

//This program finds the smallest number that is evenly divisible by all numbers from 1 to NUMBERS
int main()
{
	return getRangeLeastCommonMultiple(NUMBER);
}

bool isPrime(int number)
{
	if(number == 2)
	{
		return true;
	}
	else
	{
		for(int i=3; i<number; i+=2)
		{
			if(number %i == 0)
			{
				return false;
			}
		}
	}
	return true;
}

int getNextPrime(int number)
{
	do
	{
		++number;
	} while(!isPrime(number));
	return number;
}

std::map<int, int> getPrimeFactors(int number)
{
	std::map<int, int> factors;
	for(int i=2; number>1; i=getNextPrime(i))
	{
		while(!(number%i))
		{
			number/=i;
			if(factors.find(i)==factors.end())
			{
				factors[i]=1;
			} else
			{
				++(factors[i]);
			}
		}
	}
	return factors;
}

int getRangeLeastCommonMultiple(int maxNumber)
{
    //get the prime factor representations of all numbers from 2 to the max number
	std::vector<std::map<int,int>> primeFactorRepresentations;
        for(int i=2; i<=maxNumber; ++i)
	{
		primeFactorRepresentations.push_back(getPrimeFactors(i));
	}
	
	//get the highest exponent of each prime factor
	std::map<int, int> factorList;
	for(auto primeFactors = primeFactorRepresentations.begin();
		primeFactors != primeFactorRepresentations.end(); ++primeFactors)
	{
		for(auto factor = (*primeFactors).begin(); factor != (*primeFactors).end(); ++factor)
		{
			auto fac = factorList.find((*factor).first);
			if(fac == factorList.end())
			{
				factorList[(*factor).first] = (*factor).second;
			} 
			else if((*factor).second > (*fac).second)
			{
				factorList[(*factor).first] = (*factor).second;
			}
		}
	}
	
	int evenDivNumber = 1;
        for(auto factor = factorList.begin(); factor!= factorList.end(); ++factor)
	{
		evenDivNumber *= std::pow((double) (*factor).first, (*factor).second);
	}
	return evenDivNumber;
}