#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
using namespace std;
const int N = 1e5;
const long long mod = 1e9 + 7;
int T,A,B,C,mx,mn;
int vis[N + 5],cnt,prime[N + 5],mu[N + 5];
long long f[3][N + 5],ans;
int deg[N + 5];
vector<int> e[N + 5];
vector<long long> v[N + 5];
struct Edge
{
	int u,v,w;
} g[(N << 4) + 5];
int tot;
int main()
{
	mu[1] = 1;
	for(register int i = 2;i <= N;++i)
	{
		if(!vis[i])
			mu[prime[++cnt] = i] = -1;
		for(register int j = 1;j <= cnt && i * prime[j] <= N;++j)
		{
			vis[i * prime[j]] = 1;
			if(!(i % prime[j]))
				break;
			else
				mu[i * prime[j]] = -mu[i];
		}
	}
	memset(vis,0,sizeof vis);
	scanf("%d",&T);
	for(;T;--T)
	{
		scanf("%d%d%d",&A,&B,&C),mx = max(A,max(B,C)),mn = min(A,min(B,C)),ans = 0,memset(f,0,sizeof f);
		for(register int i = 1;i <= A;++i)
			for(register int j = i;j <= A;j += i)
				f[0][i] += A / j;
		for(register int i = 1;i <= B;++i)
			for(register int j = i;j <= B;j += i)
				f[1][i] += B / j;
		for(register int i = 1;i <= C;++i)
			for(register int j = i;j <= C;j += i)
				f[2][i] += C / j;
		for(register int i = 1;i <= mn;++i)
			mu[i] && (ans += mu[i] * mu[i] * mu[i] * f[0][i] * f[1][i] * f[2][i]);
		memset(deg,0,sizeof deg),tot = 0;
		for(register int d = 1;d <= mx;++d)
			for(register int i = 1;i * d <= mx;++i)
				if(mu[i * d])
					for(register int j = i + 1,x,y,lcm;(long long)i * j * d <= mx;++j)
						if(mu[j * d] && __gcd(i,j) == 1)
							x = i * d,y = j * d,lcm = i * j * d,
							ans += mu[x] * mu[x] * mu[y] * (
								f[0][x] * f[1][lcm] * f[2][lcm] +
								f[0][lcm] * f[1][x] * f[2][lcm] +
								f[0][lcm] * f[1][lcm] * f[2][x]),
							ans += mu[x] * mu[y] * mu[y] * (
								f[0][y] * f[1][lcm] * f[2][lcm] +
								f[0][lcm] * f[1][y] * f[2][lcm] +
								f[0][lcm] * f[1][lcm] * f[2][y]),
							++deg[x],++deg[y],g[++tot] = (Edge){x,y,lcm};
		for(register int i = 1;i <= mx;++i)
			e[i].clear(),v[i].clear();
		for(register int i = 1;i <= tot;++i)
			if(deg[g[i].u] > deg[g[i].v] || (deg[g[i].u] == deg[g[i].v] && g[i].u < g[i].v))
				e[g[i].u].push_back(g[i].v),v[g[i].u].push_back(g[i].w);
			else
				e[g[i].v].push_back(g[i].u),v[g[i].v].push_back(g[i].w);
		for(register int x = 1;x <= mx;++x)
			if(mu[x])
			{
				for(register int i = 0;i < e[x].size();++i)
					vis[e[x][i]] = v[x][i];
				for(register int i = 0,y,xy;i < e[x].size() && (y = e[x][i],xy = v[x][i],1);++i)
					if(mu[y])
						for(register int j = 0,z,xz,yz;j < e[y].size() && (z = e[y][j],xz = vis[z],yz = v[y][j],1);++j)
							if(xz && mu[z])
								ans += mu[x] * mu[y] * mu[z] * (
									f[0][xy] * f[1][xz] * f[2][yz] +
									f[0][xy] * f[1][yz] * f[2][xz] +
									f[0][xz] * f[1][xy] * f[2][yz] +
									f[0][xz] * f[1][yz] * f[2][xy] +
									f[0][yz] * f[1][xy] * f[2][xz] +
									f[0][yz] * f[1][xz] * f[2][xy]
								);
				for(register int i = 0;i < e[x].size();++i)
					vis[e[x][i]] = 0;
			}
		printf("%lld\n",ans % mod);
	}
}