Finding LCM （最小公倍数）

Finding LCM

Time Limit: 2000MS

Memory Limit: 32768KB

64bit IO Format: %lld & %llu

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Description

LCM is an abbreviation used for Least Common Multiple in Mathematics. We say LCM (a, b, c) = L if and only if L is the least integer which is divisible bya, b and c.

You will be given a, b and L. You have to find c such that LCM (a, b, c) = L. If there are several solutions, print the one where c is as small as possible. If there is no solution, report so.

Input

Input starts with an integer T (≤ 325), denoting the number of test cases.

Each case starts with a line containing three integers a b L (1 ≤ a, b ≤ 10⁶, 1 ≤ L ≤ 10¹²).

Output

For each case, print the case number and the minimum possible value of c. If no solution is found, print 'impossible'.

Sample Input

3

3 5 30

209475 6992 77086800

2 6 10

Sample Output

Case 1: 2

Case 2: 1

Case 3: impossible

 #include <iostream>
 #include <stdio.h>
 #include <string.h>
 #include <algorithm>
 using namespace std;
 long long gcd(long long x,long long y)
 {
     if(y==)return x;
     return gcd(y,x%y);
 }
 int main()
 {
     long long a,b,l;
     int n,i,j;
     cin>>n;
     for(i=; i<=n; i++)
     {
         cin>>a>>b>>l;
         a=a/gcd(a,b)*b;
         if(l%a)
         {
             printf("Case %d: ",i);
             printf("impossible\n");
         }
         else
         {
            b=l/a;
            while(gcd(a,b)!=)
            {
                long long t=gcd(a,b);
                b*=t;
                a/=t;
            }
           printf("Case %d: ",i);
             printf("%lld\n",b);
         }
     }
 }