pub mod binary_search {
    type T = usize;

    pub fn binary_search(mut ok: T, mut ng: T, f: impl Fn(T) -> bool) -> T {
        let cont = |ok: T, ng: T| {
            let l = ok.min(ng);
            let r = ok.max(ng);
            l + 1 < r
        };
        while cont(ok, ng) {
            let x = (ok + ng) / 2;
            if f(x) {
                ok = x;
            } else {
                ng = x;
            }
        }
        ok
    }
}

pub mod gcd_lcm {

    pub fn gcd(a: usize, b: usize) -> usize {
        if b == 0 {
            a
        } else {
            gcd(b, a % b)
        }
    }

    pub fn lcm(a: usize, b: usize) -> usize {
        let g = gcd(a, b);
        a / g * b
    }
}

pub mod scanner {

    pub struct Scanner {
        buf: Vec<String>,
    }

    impl Scanner {
        pub fn new() -> Self {
            Self { buf: vec![] }
        }

        pub fn new_from(source: &str) -> Self {
            let source = String::from(source);
            let buf = Self::split(source);
            Self { buf }
        }

        pub fn next<T: std::str::FromStr>(&mut self) -> T {
            loop {
                if let Some(x) = self.buf.pop() {
                    return x.parse().ok().expect("");
                }
                let mut source = String::new();
                std::io::stdin().read_line(&mut source).expect("");
                self.buf = Self::split(source);
            }
        }

        fn split(source: String) -> Vec<String> {
            source
                .split_whitespace()
                .rev()
                .map(String::from)
                .collect::<Vec<_>>()
        }
    }
}

use crate::{binary_search::binary_search, gcd_lcm::lcm, scanner::Scanner};
use std::io::Write;
fn main() {
    let mut scanner = Scanner::new();
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    let t: usize = scanner.next();
    for _ in 0..t {
        solve(&mut scanner, &mut out);
    }
}
fn solve(scanner: &mut Scanner, out: &mut std::io::BufWriter<std::io::StdoutLock>) {
    let a = scanner.next::<usize>();
    let b = scanner.next::<usize>();
    let k = scanner.next::<usize>();
    let l = lcm(a, b);
    let ans = binary_search(4e18 as usize, 0 as usize, |x| {
        let mut count = 0;
        count += x / a;
        count += x / b;
        count -= x / l;
        k <= x - count
    });
    writeln!(out, "{}", ans).unwrap();
}