#include <bits/stdc++.h>
using namespace std;
const int MOD = (int)1e9 + 7;
const int FFTMOD = 1007681537;
const int INF = (int)1e9;
const long long LINF = (long long)1e18;
const long double PI = acos((long double)-1);
const long double EPS = 1e-9;
inline long long gcd(long long a, long long b) {
  long long r;
  while (b) {
    r = a % b;
    a = b;
    b = r;
  }
  return a;
}
inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
inline long long fpow(long long n, long long k, int p = MOD) {
  long long r = 1;
  for (; k; k >>= 1) {
    if (k & 1) r = r * n % p;
    n = n * n % p;
  }
  return r;
}
template <class T>
inline int chkmin(T& a, const T& val) {
  return val < a ? a = val, 1 : 0;
}
template <class T>
inline int chkmax(T& a, const T& val) {
  return a < val ? a = val, 1 : 0;
}
inline long long isqrt(long long k) {
  long long r = sqrt(k) + 1;
  while (r * r > k) r--;
  return r;
}
inline long long icbrt(long long k) {
  long long r = cbrt(k) + 1;
  while (r * r * r > k) r--;
  return r;
}
inline void addmod(int& a, int val, int p = MOD) {
  if ((a = (a + val)) >= p) a -= p;
}
inline void submod(int& a, int val, int p = MOD) {
  if ((a = (a - val)) < 0) a += p;
}
inline int mult(int a, int b, int p = MOD) { return (long long)a * b % p; }
inline int inv(int a, int p = MOD) { return fpow(a, p - 2, p); }
inline int sign(long double x) { return x < -EPS ? -1 : x > +EPS; }
inline int sign(long double x, long double y) { return sign(x - y); }
const int maxn = 1e6 + 5;
const int maxx = 2e7 + 5;
int sp[maxn];
int x, p, k;
vector<int> vals;
int f[1 << 20];
long long calc(long long n) {
  long long res = n;
  for (int msk = (1); msk < (1 << int((vals).size())); ++msk) {
    if (__builtin_popcountll(msk) & 1) {
      res -= n / f[msk];
    } else {
      res += n / f[msk];
    }
  }
  return res;
}
void chemthan() {
  for (int i = (1); i < (maxn); ++i) sp[i] = i;
  for (int i = (2); i < (maxn); ++i)
    if (sp[i] == i) {
      for (int j = i + i; j < maxn; j += i) {
        chkmin(sp[j], i);
      }
    }
  int test;
  cin >> test;
  while (test--) {
    cin >> x >> p >> k;
    int t = p;
    vals.clear();
    while (t > 1) {
      int nt = sp[t];
      if (!int((vals).size()) || vals.back() != nt) {
        vals.push_back(nt);
      }
      t /= nt;
    }
    for (int msk = (0); msk < (1 << int((vals).size())); ++msk) {
      f[msk] = 1;
      for (int i = (0); i < (int((vals).size())); ++i)
        if ((((msk) >> (i)) & 1)) {
          f[msk] *= vals[i];
        }
    }
    long long lo = 0, hi = INF;
    while (lo < hi) {
      long long mi = lo + hi >> 1;
      if (calc(mi) - calc(x) < k) {
        lo = mi + 1;
      } else {
        hi = mi;
      }
    }
    cout << (lo + hi >> 1) << "\n";
  }
}
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(0), cin.tie(0);
  if (argc > 1) {
    assert(freopen(argv[1], "r", stdin));
  }
  if (argc > 2) {
    assert(freopen(argv[2], "wb", stdout));
  }
  chemthan();
  cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
  return 0;
}
