# coding: utf-8
# Your code here!

T=int(input())

for _ in range(T):
    A,B,K=map(int,input().split())
    
    high=3*10**18
    low=-1
    
    while high-low>1:
        middle=(high+low)//2
        
        yaku_A=middle//A
        yaku_B=middle//B
        yaku_AB=middle//(A*B)
        
        all_unyaku=middle-yaku_A-yaku_B+yaku_AB
        
        if all_unyaku>=K:
            high=middle
        else:
            low=middle
    
    print(high)