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