| Time Limit: 2000MS | Memory Limit: 32768KB | 64bit IO Format: %lld & %llu |
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);
}
}
}