Ugly Number III

# Python
from math import gcd

def nthUglyNumber(n, a, b, c):
    def lcm(x, y): return x * y // gcd(x, y)
    ab = lcm(a, b); ac = lcm(a, c); bc = lcm(b, c); abc = lcm(ab, c)

    def count(x):
        return x//a + x//b + x//c - x//ab - x//ac - x//bc + x//abc

    lo, hi = 1, 2 * 10**9
    while lo < hi:
        mid = (lo + hi) // 2
        if count(mid) >= n:
            hi = mid
        else:
            lo = mid + 1
    return lo

// C++
long long gcd(long long a, long long b){ return b?gcd(b,a%b):a; }
long long lcm(long long a, long long b){ return a/gcd(a,b)*b; }
int nthUglyNumber(int n, int a, int b, int c) {
    long long ab=lcm(a,b),ac=lcm(a,c),bc=lcm(b,c),abc=lcm(ab,c);
    auto count=[&](long long x){ return x/a+x/b+x/c-x/ab-x/ac-x/bc+x/abc; };
    long long lo=1,hi=2e9;
    while(lo<hi){long long mid=(lo+hi)/2;if(count(mid)>=n)hi=mid;else lo=mid+1;}
    return lo;
}

// Java
long gcd(long a, long b){ return b==0?a:gcd(b,a%b); }
long lcm(long a, long b){ return a/gcd(a,b)*b; }
public int nthUglyNumber(int n, int a, int b, int c) {
    long ab=lcm(a,b),ac=lcm(a,c),bc=lcm(b,c),abc=lcm(ab,c);
    long lo=1,hi=2000000000L;
    while(lo<hi){
        long mid=(lo+hi)/2;
        long cnt=mid/a+mid/b+mid/c-mid/ab-mid/ac-mid/bc+mid/abc;
        if(cnt>=n)hi=mid;else lo=mid+1;
    }
    return (int)lo;
}

// JavaScript
function nthUglyNumber(n, a, b, c) {
    const gcd = (x, y) => y ? gcd(y, x%y) : x;
    const lcm = (x, y) => x / gcd(x, y) * y;
    const ab=lcm(a,b),ac=lcm(a,c),bc=lcm(b,c),abc=lcm(ab,c);
    const count = x => Math.floor(x/a)+Math.floor(x/b)+Math.floor(x/c)-Math.floor(x/ab)-Math.floor(x/ac)-Math.floor(x/bc)+Math.floor(x/abc);
    let lo=1n,hi=2000000000n;
    // Use number version
    let lo2=1,hi2=2e9;
    while(lo2<hi2){const mid=Math.floor((lo2+hi2)/2);if(count(mid)>=n)hi2=mid;else lo2=mid+1;}
    return lo2;
}