import math

T = int(input())
ans = [0]*T

for i in range(T):
    a, b, k = map(int, input().split())
    l = a*b//math.gcd(a, b)
    lo = 1
    hi = 1000000000000000000000
    mid = 0
    while hi-lo>1:
        mid = (lo + hi)//2
        cnt = mid//a + mid//b - mid//l
        if mid-cnt<=k:
            lo = mid
        else:
            hi = mid
    ans[i] = lo

for i in range(T):
    print(ans[i])