from random import getrandbits, randrange
from string import ascii_lowercase, ascii_uppercase
import sys
from math import ceil, floor, sqrt, pi, factorial, gcd, log, log10, log2, inf, cos, sin
from copy import deepcopy, copy
from collections import Counter, deque, defaultdict
from heapq import heapify, heappop, heappush
from itertools import (
    accumulate,
    product,
    combinations,
    combinations_with_replacement,
    permutations,
)
from bisect import bisect, bisect_left, bisect_right
from functools import lru_cache, reduce
from decimal import Decimal, getcontext
from typing import List, Tuple, Optional


inf = float("inf")


def ceil_div(a, b):
    return (a + b - 1) // b


def isqrt(num):
    res = int(sqrt(num))
    while res * res > num:
        res -= 1
    while (res + 1) * (res + 1) <= num:
        res += 1
    return res


def int1(s):
    return int(s) - 1


from types import GeneratorType


def bootstrap(f, stack=[]):
    def wrapped(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to

    return wrapped


import sys
import os
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


print = lambda *args, end="\n", sep=" ": sys.stdout.write(
    sep.join(map(str, args)) + end
)


def II():
    return int(input())


def MII(base=0):
    return map(lambda s: int(s) - base, input().split())


def LII(base=0):
    return list(MII(base))


def NA():
    n = II()
    a = LII()
    return n, a


def read_graph(n, m, base=0, directed=False, return_edges=False):

    g = [[] for _ in range(n)]
    edges = []
    for _ in range(m):
        a, b = MII(base)
        if return_edges:
            edges.append((a, b))
        g[a].append(b)
        if not directed:
            g[b].append(a)
    if return_edges:
        return g, edges
    return g


def read_graph_with_weight(n, m, base=0, directed=False, return_edges=False):

    g = [[] for _ in range(n)]
    edges = []
    for _ in range(m):
        a, b, w = MII()
        a, b = a - base, b - base
        if return_edges:
            edges.append((a, b, w))
        g[a].append((b, w))
        if not directed:
            g[b].append((a, w))
    if return_edges:
        return g, edges
    return g


def yes(res):
    print("Yes" if res else "No")


def YES(res):
    print("YES" if res else "NO")


def cmin(dp, i, x):
    if x < dp[i]:
        dp[i] = x


def cmax(dp, i, x):
    if x > dp[i]:
        dp[i] = x


def alp_a_to_i(s):
    return ord(s) - ord("a")


def alp_A_to_i(s):
    return ord(s) - ord("A")


def alp_i_to_a(i):
    return chr(ord("a") + i)


def alp_i_to_A(i):
    return chr(ord("A") + i)


d4 = [(1, 0), (0, 1), (-1, 0), (0, -1)]
d8 = [(1, 0), (1, 1), (0, 1), (-1, 1), (-1, 0), (-1, -1), (0, -1), (1, -1)]


def ranges(n, m):
    return ((i, j) for i in range(n) for j in range(m))


def valid(i, j, n, m):
    return 0 <= i < n and 0 <= j < m


def ninj(i, j, n, m):
    return [(i + di, j + dj) for di, dj in d4 if valid(i + di, j + dj, n, m)]


def gen(x, *args):
    if len(args) == 1:
        return [x] * args[0]
    if len(args) == 2:
        return [[x] * args[1] for _ in [0] * args[0]]
    if len(args) == 3:
        return [[[x] * args[2] for _ in [0] * args[1]] for _ in [0] * args[0]]
    if len(args) == 4:
        return [
            [[[x] * args[3] for _ in [0] * args[2]] for _ in [0] * args[1]]
            for _ in [0] * args[0]
        ]


list2d = lambda a, b, v: [[v] * b for _ in range(a)]
list3d = lambda a, b, c, v: [[[v] * c for _ in range(b)] for _ in range(a)]


class Debug:
    def __init__(self, debug=False):
        self.debug = debug
        cur_path = os.path.dirname(os.path.abspath(__file__))
        self.local = os.path.exists(cur_path + "/.cph")

    def get_ic(self):
        if self.debug and self.local:
            from icecream import ic

            return ic
        else:
            return lambda *args, **kwargs: ...


def lcm(*args):
    if len(args) < 2:
        raise ValueError("At least two numbers are required to calculate LCM.")

    result = abs(args[0])
    for i in range(1, len(args)):
        result = abs(result * args[i]) // gcd(result, args[i])
    return result


def pairwise(a):
    n = len(a)
    for i in range(n - 1):
        yield a[i], a[i + 1]


def factorial(n):
    return reduce(lambda x, y: x * y, range(1, n + 1))


ic = Debug(1).get_ic()

T = 1
T = II()
for _ in range(T):
    a, b, k = MII()

    def check(mid):
        return mid - mid // a - mid // b + mid // lcm(a, b) >= k

    l = 1
    r = 1
    while not check(r):
        l = r
        r *= 10
    res = r
    while l <= r:
        mid = (l + r) // 2
        if check(mid):
            r = mid - 1
            res = mid
        else:
            l = mid + 1
    print(res)