#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 1000000007;
using Mint = ModInt<MO>;


/*
  (p^e0, p^e1, p^e2) -> e0+e1+e2+1
  \sum[e0,e1,e2>=0] (e0+e1+e2+1) x0^e0 x1^e1 x2^e2
  = x0/(1-x0)^2(1-x1)(1-x2) + x1/(1-x0)(1-x1)^2(1-x2) + x2/(1-x0)(1-x1)(1-x2)^2 + 1/(1-x0)(1-x1)(1-x2)
  = 1/(1-x0)^2(1-x1)^2(1-x2)^2 (1 - x0x1 - x0x2 - x1x2 + 2x0x1x2)
*/

int A, B, C;
int N;
vector<int> lpf, primes;

vector<Mint> wtsA, wtsB, wtsC;
Int counter;
Mint ans;

void dfs(int i, int a, int b, int c, Mint t) {
++counter;
  ans += t * wtsA[a] * wtsB[b] * wtsC[c];
  for (; ++i < (int)primes.size(); ) {
    const Int p = primes[i];
    const Int aa = a * p, bb = b * p, cc = c * p;
    if ((aa > A) + (bb > B) + (cc > C) >= 2) break;
    if (aa <= A && bb <= B) dfs(i, aa, bb, c, -t);
    if (aa <= A && cc <= C) dfs(i, aa, b, cc, -t);
    if (bb <= B && cc <= C) dfs(i, a, bb, cc, -t);
    if (aa <= A && bb <= B && cc <= C) dfs(i, aa, bb, cc, t + t);
  }
}

int main() {
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    scanf("%d%d%d", &A, &B, &C);
    
    N = max({A, B, C});
    lpf.assign(N + 1, 0);
    primes.clear();
    for (int p = 2; p <= N; ++p) lpf[p] = p;
    for (int p = 2; p <= N; ++p) if (lpf[p] == p) {
      primes.push_back(p);
      for (int n = p; n <= N; n += p) chmin(lpf[n], p);
    }
    
    vector<int> Sigma0(N + 1, 0);
    for (int d = 1; d <= N; ++d) for (int n = d; n <= N; n += d) ++Sigma0[n];
    for (int n = 1; n <= N; ++n) Sigma0[n] += Sigma0[n - 1];
    wtsA.resize(A + 1);
    wtsB.resize(B + 1);
    wtsC.resize(C + 1);
    for (int n = 1; n <= A; ++n) wtsA[n] = Sigma0[A / n];
    for (int n = 1; n <= B; ++n) wtsB[n] = Sigma0[B / n];
    for (int n = 1; n <= C; ++n) wtsC[n] = Sigma0[C / n];
    
counter=0;
    ans = 0;
    dfs(-1, 1, 1, 1, 1);
cerr<<"A = "<<A<<", B = "<<B<<", C = "<<C<<": counter = "<<counter<<endl;
    printf("%u\n", ans.x);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}