#![allow(non_snake_case, unused_imports, unused_must_use)]
use std::io::{self, prelude::*};
use std::str;

fn main() {
    let (stdin, stdout) = (io::stdin(), io::stdout());
    let mut scan = Scanner::new(stdin.lock());
    let mut out = io::BufWriter::new(stdout.lock());

    macro_rules! input {
        ($T: ty) => {
            scan.token::<$T>()
        };
        ($T: ty, $N: expr) => {
            (0..$N).map(|_| scan.token::<$T>()).collect::<Vec<_>>()
        };
    }

    let T = input!(usize);

    for _ in 0..T {
        // TODO: (2, 3, 10^18) を試してみたほうがよさそう -> できてそう
        let A = input!(usize);
        let B = input!(usize);
        let K = input!(usize);

        let G = gcd(A, B);
        let L = A * B / G;

        // let a = L / A;
        // let b = L / B;

        // let dc = L + 1 - a - b;

        let mut left = 0;
        let mut right = usize::MAX;

        while right - left > 1 {
            let mid = (right + left) / 2;

            let cnt = mid + (mid / L) - (mid / A) - (mid / B);

            // writeln!(out, "{} {} {} {}", left, right, mid, cnt);

            if cnt >= K {
                right = mid;
            } else {
                left = mid;
            }
        }

        writeln!(out, "{}", right);
    }
}

fn gcd(a: usize, b: usize) -> usize {
    if a < b {
        return gcd(b, a);
    }

    if b == 0 {
        return a;
    } else {
        return gcd(b, a % b);
    }
}

struct Scanner<R> {
    reader: R,
    buf_str: Vec<u8>,
    buf_iter: str::SplitWhitespace<'static>,
}
impl<R: BufRead> Scanner<R> {
    fn new(reader: R) -> Self {
        Self {
            reader,
            buf_str: vec![],
            buf_iter: "".split_whitespace(),
        }
    }
    fn token<T: str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buf_iter.next() {
                return token.parse().ok().expect("Failed parse");
            }
            self.buf_str.clear();
            self.reader
                .read_until(b'\n', &mut self.buf_str)
                .expect("Failed read");
            self.buf_iter = unsafe {
                let slice = str::from_utf8_unchecked(&self.buf_str);
                std::mem::transmute(slice.split_whitespace())
            }
        }
    }
}