Lightoj 1215 Finding LCM (number theory)

Test instructions The LCM (a, b, c) = L and A, B, l are known to be the least satisfying equation C.

After the number is expanded into the form of a factor product

GCD (A, A, b) is the lesser exponent of the common factor

The LCM (A, A, a, b) is the larger exponent of all the element factors in a

Make M = LCM (A, B) the problem translates in order to find the smallest C-satisfied LCM (M, c) = L

So the smallest c is the element factor in L that is not in M and L medium exponent is greater than m, and the exponent in L is the product

#include <bits/stdc++.h>
Using namespace std;
Typedef long long ll;

Ll gcd(ll a, ll b)
{
    Return b ? gcd(b, a % b) : a;
}

Int main()
{
    Int T;
    Ll a, b, l, c, d, m;
    Scanf("%d", &T);
    For(int cas = 1; cas <= T; ++cas)
    {
        Printf("Case %d: ", cas);
        Scanf("%lld%lld%lld", &a, &b, &l);
        m = a * b / gcd(a, b); //m is the greatest common divisor of a, b

        If(l % m) puts("impossible");
        Else
        {
            / / To make lcm (c, m) = l c at least have a prime factor in l not in m and l index in the index greater than m in the index in l
            c = l / m; // Now c contains the prime factor in l that is not in m, and the exponent in l is greater than the prime factor in m.
            // Then c now needs to multiply the public prime factor of c and m to take the index in m
            While((d = gcd(c, m)) != 1) //gcd(c,m) takes a small exponential product of c,m common prime factors
            {
                c = c * d, m = m / d;
                d = gcd(c, m);
            }
            Printf("%lld\n", c);
        }
    }
    Return 0;
} 

1215-finding LCM

LCM is a abbreviation used for LEast Common Multiple in mathematics. We say LCM (A, b, c) = L if and only if L are the least integer which is divisible by a, B and C7>c.

You'll be given a, B and L. You have the to find C such. LCM (A, b, c) = L. If There is several solutions, print the one where C is as small as possible. If there is no solution.

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	Output for Sample Input
3 3 5 30 209475 6992 77086800 2 6 10	Case 1:2 Case 2:1 Case 3:impossible

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Lightoj 1215 Finding LCM (number theory)