#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
template <typename T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T, class T1>
inline void gn(T &first, T1 &second) {
  gn(first);
  gn(second);
}
template <class T, class T1, class T2>
inline void gn(T &first, T1 &second, T2 &z) {
  gn(first);
  gn(second);
  gn(z);
}
template <typename T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <typename T>
inline void println(T first) {
  print(first), putchar('\n');
}
template <typename T>
inline void printsp(T first) {
  print(first), putchar(' ');
}
template <class T, class T1>
inline void print(T first, T1 second) {
  printsp(first), println(second);
}
template <class T, class T1, class T2>
inline void print(T first, T1 second, T2 z) {
  printsp(first), printsp(second), println(z);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
int vst[1000100];
void pre() {
  for (int i = 2; i < 1000100; i++) {
    if (vst[i]) continue;
    vst[i] = i;
    if (i > 10000) continue;
    for (int j = i * i; j < 1000100; j += i) {
      if (!vst[j]) vst[j] = i;
    }
  }
}
int cnt, q[20], mul[1 << 20];
void pre(int p) {
  cnt = 0;
  while (p > 1) {
    q[cnt] = vst[p];
    while (p % q[cnt] == 0) p /= q[cnt];
    cnt++;
  }
  mul[0] = 1;
  for (int i = 1; i < 1 << cnt; i++)
    mul[i] = mul[i - (1 << (__builtin_ctz(i)))] * q[(__builtin_ctz(i))];
}
long long calc(long long n) {
  long long ans = 0;
  for (int i = 0; i < 1 << cnt; i++) {
    if ((__builtin_popcount(i)) & 1)
      ans -= n / mul[i];
    else
      ans += n / mul[i];
  }
  return ans;
}
int main() {
  pre();
  int T, first, p, k;
  for (gn(T); T--;) {
    gn(first, p, k);
    if (p == 1) {
      println(first + k);
      continue;
    }
    pre(p);
    k += calc(first);
    long long L = first, R = 1LL << 60, mid;
    while (R - L > 1) {
      mid = L + R >> 1;
      if (calc(mid) < k)
        L = mid;
      else
        R = mid;
    }
    println(R);
  }
  return 0;
}
