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
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
1 #include <iostream> 2 #include <stdio.h> 3 #include <string.h> 4 #include <algorithm> 5 using namespace std; 6 long long gcd(long long x,long long y) 7 { 8 if(y==0)return x; 9 return gcd(y,x%y); 10 } 11 int main() 12 { 13 long long a,b,l; 14 int n,i,j; 15 cin>>n; 16 for(i=1; i<=n; i++) 17 { 18 cin>>a>>b>>l; 19 a=a/gcd(a,b)*b; 20 if(l%a) 21 { 22 printf("Case %d: ",i); 23 printf("impossible "); 24 } 25 else 26 { 27 b=l/a; 28 while(gcd(a,b)!=1) 29 { 30 long long t=gcd(a,b); 31 b*=t; 32 a/=t; 33 } 34 printf("Case %d: ",i); 35 printf("%lld ",b); 36 } 37 } 38 }