%ProjectEuler/Problem5.m
%This is a script to answer Problem 5 for Project Euler
%What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

%Create your variables
nums = [1:20];
factors = [1];	%The factors that are already in the number
list = [];	%For a temperary list of the factors of the current number
counter = 1;

%You need to find the factors of all the numbers from 1->20
while(counter <= size(nums)(2))
	list = factor(nums(counter));

	%Search factors and try to match all elements in list
	listCnt = 1;
	factorCnt = 1;
	while(listCnt <= size(list)(2))
		if((factorCnt > size(factors)(2)) || (factors(factorCnt) > list(listCnt)))
			%If it was not found add the factor to the list for the number and reset the counters
			factors(end + 1) = list(listCnt);
			factors = sort(factors);
			factorCnt = 1;
			listCnt = 1;
		elseif(factors(factorCnt) == list(listCnt))
			++listCnt;
			++factorCnt;
		else
			++factorCnt;
		end
	end
	++counter;
end

prod(factors)

%Cleanup your variables
clear counter;
clear factorCnt;
clear listCnt;
clear list;
clear nums;
clear factors;