use std::io::Write;

fn run() {
    input! {
        t: usize,
        ask: [(u64, u64, u64); t],
    }
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    for (mut p, mut q, k) in ask {
        let g = gcd(p, q);
        p /= g;
        q /= g;
        if p > q {
            std::mem::swap(&mut p, &mut q);
        }
        if p == 1 {
            writeln!(out, "{}", k * g).ok();
            continue;
        }
        let n = (p - 1) * (q - 1) - 1;
        let u = n / q;
        let cnt = u + floor_sum(u + 1, p, q, n - q * u);
        if cnt < k {
            writeln!(out, "{}", g * ((p - 1) * (q - 1) + k - cnt - 1)).ok();
            continue;
        }
        let mut ok = n;
        let mut ng = 0;
        while ok - ng > 1 {
            let mid = (ok + ng) / 2;
            let u = mid / q;
            let cnt = u + floor_sum(u + 1, p, q, mid - q * u);
            if cnt >= k {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        writeln!(out, "{}", ok).ok();
    }
}

fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}

fn main() {
    run();
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

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

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------
// ---------- begin floor sum ----------
// sum_{i = 0}^{n - 1} floor((ai + b) / m)
pub fn floor_sum(n: u64, m: u64, mut a: u64, mut b: u64) -> u64 {
    assert!(n <= 10u64.pow(9));
    assert!(1 <= m && m <= 10u64.pow(9));
    let mut ans = 0;
    ans += a / m * n * (n - 1) / 2 + b / m * n;
    a %= m;
    b %= m;
    let p = a * n + b;
    if p >= m {
        ans += floor_sum(p / m, a, m, p % m);
    }
    ans
}
// ---------- end floor sum ----------