LightOj 1215 - Finding LCM

 // Verdict:: Accepted
#include <iostream>
#include <cstdio>
#include <cstring>
#include <map>
#include <string>
#include <vector>
#include <cmath>
#include <cctype>
#include <sstream>
#include <set>
#include <list>
#include <stack>
#include <queue>
#include <algorithm>
#define sf scanf
#define pf printf
#define sfint(a,b) scanf("%d %d",&a,&b)
#define sfl(a,b) scanf("%ld %ld",&a,&b)
#define sfll(a,b) scanf("%lld %lld",&a,&b)
#define sfd(a,b) scanf("%lf %lf",&a,&b)
#define sff(a,b) scanf("%f %f",&a,&b)
#define lp1(i,n) for(i=0;i<n;i++)
#define lp2(i,n) for(i=1;i<=n;i++)
#define LL long long
#define L long
#define mem(c,v) memset(c,v,sizeof(c))
#define ui unsigned int
#define cp(a) cout<<" "<<a<<" "<<endl
#define ull unsigned long long int
#define nl puts("")
#define sq(x) ((x)*(x))
#define all(x) x.begin(),x.end()
#define mx7 20000100
#define mx6 1500000
#define mx5 100005
#define inf 1<<30                                           //infinity value
#define eps 1e-9
#define mx (65540)
#define mod 1000000007
#define pb push_back
#define pi acos(-1.0)
#define sz size()
#define gc getchar ()


using namespace std;
//..................................................................................................................

template<class T> T setbit(T n, T pos){n=n|(1<<pos); return n;}
template<class T> T checkbit(T n, T pos){n=n&(1<<pos); return n;}
template<class T> T gcd(T a, T b ) {return b<=0?a:gcd(b,a%b);}
template<class T> T lcm(T a, T b) {return ((a / gcd(a,b) ) * b);}
template<class T> T large(T a, T b ) {return a>b?a:b;}
template<class T> T small(T a, T b ) {return a<b?a:b;}

int main()
{
    int tc,t=0;
    sf("%d",&tc);

    while(tc--)
    {
        ull a,b,x;
        sf("%llu %llu %llu",&a,&b,&x);

        ull r = lcm<ull>(a,b); //cout << r;

        if(!(x % r))
        {
            ull c = x / r;
            ull ans,d=gcd(c,x);

            if(d==1)
            {
                pf("Case %d: %llu\n",++t,c);
            }

            else
            {
                ans=1;

                while(d != 1)
                {
                    d=gcd(c,x);
                    x/=d;
                    ans*=d;
                }

                pf("Case %d: %llu\n",++t,ans);
            }
        }

        else
        {
            pf("Case %d: impossible\n",++t);
        }
    }

    return 0;
}

---

---

================       **** Recursion Manner  ****============================

 
// Verdict:: Accepted
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <vector>
#include <map>
#include <string>
#include <algorithm>
#define sf scanf
#define pf printf
#define LL long long
#define Lo long
#define ull unsigned long long
#define ul unsigned long
#define ui unsigned int
#define mx 1000100

using namespace std;

template<class T> T gcd(T a, T b){return b<=0?a:gcd(b,a%b);}
template<class T> T lcm(T a, T b){return (a / (gcd(a,b))) * b; }
template<class T> T setbit(T n, T pos) {return (n|(1<<pos));}
template<class T> T checkbit(T n, T pos) {return (n&(1<<pos));}

LL find_one(LL c, LL L)
{
    LL d=gcd<LL>(c,L),ans=1;
    //LL d;
    //cout << "c = " << c << endl;
    //cout << "d = " << d << endl;
    L=L/d;
    //cout << "L = " << L << endl;

    if(gcd<LL>(c,L)==1) return d;

    //else
    //{
        //ans*=d;
        d = d * find_one(c , L);

    //}

    //cout << "d = " << d;
    return d;
}


int main()
{
    int tc,t=0;
    cin >> tc;

    while(tc--)
    {
        LL a,b,L;
        sf("%lld %lld %lld",&a,&b,&L);

        LL res=lcm<LL>(a,b); //cout << "res = " << res;

        LL modo=L%res;
        LL take;

        if(!modo)
        {

            LL divi=L/res;
            LL c=gcd<LL>(divi,L);
            //cout << "c = " << c;

            if(c==1)
            {
                pf("Case %d: %lld\n",++t,L/res);
            }

            else
            {
                //cout << "c = " << c << endl;
                //cout << "L = " << L << endl;
                LL take=find_one(c,L);
                //find_one(c,L);
                pf("Case %d: %lld\n",++t,take);
            }

            //pf("Case %d: %lld\n",++t,take);
        }

        else
        {
            pf("Case %d: impossible\n",++t);
        }

    }

    return 0;
}