Project Euler: Solution for Problem 5

 1 #include<iostream>
 2 #include<string>
 3 #include<vector>
 4 #include<cmath>
 5 using namespace std;
 6     
 7 int fac(int origin, int comps, vector<int> prs);
 8 
 9 void main()
10 {
11     const int num = 20;　　
12     int pr_product = 1;　　//the result stores in this varaiable
13     vector<int> pr;　　//vector containing all prime numbers in range (0,20)
14     vector<int> compo;　　//vector containing all composite numbers in range (0,20)
15     //find out all prime numbers among 1-20
16     for(int i = 2; i < (num + 1); i++){
17         bool isPr = true;
18         for(int cnt = 2; cnt < i; cnt++){
19             if( i%cnt == 0){
20                 isPr = false;
21                 break;
22             }
23         }
24         if(isPr){　　//prime numbers push into vector pr
25             pr_product *= i;
26             pr.push_back(i);
27         }else{　　　　//composite numbers push into vector compo
28             compo.push_back(i);
29         }
30     }
31     for(int i = 0; i < compo.size(); i++){　　//For each composite number which the result we have now cannot divide
32         if(pr_product%compo[i] != 0)　　　　　　//determine lowest common multiple
33             pr_product = fac(pr_product, compo[i], pr);
34     }
35     cout<<pr_product<<endl;
36 }
37 
38 int fac(int origin, int comps, vector<int> prs){　　//determine lowest common multiple
39     int record = 1;
40     for(int i = 0; comps > prs[i]; i++){
41         while( (origin%prs[i] == 0) && (comps%prs[i] == 0) ){
42             record *= prs[i];
43             origin /= prs[i];
44             comps /= prs[i];
45         }
46     }
47     return record = origin * comps * record;
48 }