#![allow(unused_imports, dead_code, unused_macros, unused_variables, non_snake_case, unused_parens)]
use std::cmp::{min,max,Ordering,Reverse};
use std::mem::swap;
use std::collections::{VecDeque,LinkedList,HashMap,BTreeMap,HashSet,BTreeSet,BinaryHeap};

const MOD:u64 = 1_000_000_007;
const INF:i64 = 0x7fff_ffff_ffff_ffff;

macro_rules! min {($a:expr $(,)*) => {{$a}};($a:expr, $b:expr $(,)*) => {{std::cmp::min($a, $b)}};($a:expr, $($rest:expr),+ $(,)*) => {{std::cmp::min($a, min!($($rest),+))}};}
macro_rules! max {($a:expr $(,)*) => {{$a}};($a:expr, $b:expr $(,)*) => {{std::cmp::max($a, $b)}};($a:expr, $($rest:expr),+ $(,)*) => {{std::cmp::max($a, max!($($rest),+))}};}
macro_rules! mulvec {($x:expr; $s:expr) => {vec![$x; $s]};($x:expr; $s0:expr; $( $s:expr );+) => {mulvec![vec![$x; $s0]; $( $s );+ ]};}

use std::ops::*;

pub fn gcd<T>(mut a: T, mut b: T) -> T
where T: Copy + Default + PartialOrd + Rem<Output = T>
{
	if a < b { (a,b) = (b,a);}
	while b != T::default() {
		(a,b) = (b, a%b);
	}
	a
}


fn func(a:usize, b:usize, x:usize) -> usize {
	let g = gcd(a, b);
	let l = a / g * b;
	let mut ret: usize = x;
	let ag = a/g;
	let bg = b/g;
	ret -= x / l * (ag + bg - 1);
	let r = x % l;
	ret -= r / a + r / b;
	ret
}

fn solve() {
    input! {
        t: usize,
		ABK:[(usize,usize,usize);t],
    }
    for (a,b,k) in ABK {
		let (mut l, mut r) = (0, 8e18 as usize);
		while l+1 < r {
			let m = l+r>>1;
			if func(a, b, m) > k {
				r = m;
			}else {
				l = m;
			}
		}
		println!("{}", l);
	}
}

fn main() {
    std::thread::Builder::new()
        .stack_size(128 * 1024 * 1024)
        .spawn(|| solve()).unwrap()
        .join().unwrap();
}


mod _input {
    // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
    #[macro_export]
    macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut iter = $s.split_whitespace();
            let mut next = || { iter.next().unwrap() };
            input_inner!{next, $($r)*}
        };
        ($($r:tt)*) => {
            let stdin = std::io::stdin();
            let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
            let mut next = move || -> String{
                bytes
                    .by_ref()
                    .map(|r|r.unwrap() as char)
                    .skip_while(|c|c.is_whitespace())
                    .take_while(|c|!c.is_whitespace())
                    .collect()
            };
            input_inner!{next, $($r)*}
        };
    }
    #[macro_export]
    macro_rules! input_inner {
        ($next:expr) => {};
        ($next:expr, ) => {};

        ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
            let $var = read_value!($next, $t);
            input_inner!{$next $($r)*}
        };
    }
    #[macro_export]
    macro_rules! read_value {
        ($next:expr, ( $($t:tt),* )) => {
            ( $(read_value!($next, $t)),* )
        };

        ($next:expr, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        };

        ($next:expr, chars) => {
            read_value!($next, String).chars().collect::<Vec<char>>()
        };

        ($next:expr, usize1) => {
            read_value!($next, usize) - 1
        };

        ($next:expr, $t:ty) => {
            $next().parse::<$t>().expect("Parse error")
        };
    }
}