package main

import . "fmt"
import . "math/big"
import . "os"
import bf "bufio"

func main() {
	rd := bf.NewReader(Stdin)
	var t int
	Fscan(rd, &t)
	for ; t > 0 ; t-- {
		var a,b,k int64
		Fscan(rd,&a,&b,&k)
		ans := solve(a, b, k)
		Println(ans)
	}
}

func solve(a, b, k int64) int64 {
	gcd := new(Int).GCD(nil,nil,NewInt(a),NewInt(b)).Int64()
	lcm := a/gcd*b
	var lb, ub int64 = 0, 1<<62-1
	for lb+1 < ub {
		mid := (lb+ub)/2
		c := mid-mid/a-mid/b+mid/lcm
		if c < k {
			lb = mid
		} else {
			ub = mid
		}
	}
	return ub
}

func init() {
	// check()
}

func check() {
	var a, b, k int64
	for a = 2; a < 100; a++ {
		for b = a+1; b < 100; b++ {
			for k = 1; k < 100; k++ {
				s1 := solve(a, b, k)
				s2 := bruteforce(a, b, k)
				if s1 != s2 {
					panic(Sprintf(
						"a=%d,b=%d,k=%d,s1=%d,s2=%d",
						a,b,k,s1,s2,
					))
				}
			}
		}
	}
}

func bruteforce(a, b, k int64) int64 {
	for i := int64(1); ; i++ {
		if i % a == 0 || i % b == 0 {
			continue
		}
		k--
		if k == 0 {
			return i
		}
	}
	return -1
}