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Numbers II

                               Numbers II

                                              Binary Search


#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;

ll findTerm(ll a, ll b, ll lcm, ll value)
{
    return (value / a) + (value / b) - (value / lcm);
}

ll  solve(ll a, ll b, ll n)
{
    ll gcd  = __gcd(a,b);
    ll lcm = (a * b) / gcd;

    ll rema = lcm / a;
    ll remb = lcm / b;
    ll low = (n / (rema + remb - 1))  * lcm;
    ll high = min(a, b) * n;
    ll ans;

    while(low <= high)
    {
        ll mid = (low + high) / 2;
        ll term = findTerm(a, b, lcm, mid);

        if(term >= n)
        {
            ans = mid;
            high = mid - 1;
        }
        else
        {
            low = mid + 1;
        }
    }

    return ans;

}

int main()
{
    int t;
    ll a, b, n;

    cin >> t;
    while(t--)
    {
        cin >> a >> b >> n;

        cout << solve(a, b, n) << endl;
    }

    return 0;
}

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