寻找n个数中k个数的最小公倍数

给定一个数组，其中含有n个整数，还给定一个整数X，可以从n个数中选取任意个数的元素，使这些元素的最小公倍数为X，如果存在则返回Possible,否则返回Impossible.

#include <algorithm>
#include <stdio.h>
#include <stdlib.h>
#include <iomanip>
#include <string>
#include <string.h>
#include <math.h>
#include <queue>
#include <map>
#include <stack>
#include <vector>
#include <iostream>

using namespace std;
# define LL long long int

class LCMSetEasy
{
public:

	LL gcd(LL a, LL b) { return a%b == 0 ? b : gcd(b,a%b);}
	LL lcm(LL a, LL b) { return a * b / gcd(a, b);}

	string include(vector <int> S, int x)
	{
		int i;
		LL tar = 1;
		for(i = 0; i < S.size(); i++)
		{
			if(x % S[i] == 0)
			{
				tar = lcm(tar, S[i]);
				if(tar > x) return "Impossible";
			}
		}
		if(tar == x) return "Possible";
		return "Impossible";
	}
};

int main()
{
	LCMSetEasy test;
	vector<int> vec;
	vec.push_back(9788);
	vec.push_back(8418);
	vec.push_back(10);
	vec.push_back(35);
	vec.push_back(55);
	vec.push_back(7250);
	cout<<test.include(vec,37683800)<<endl;

	return 0;
}