1201

class Solution:
    def nthUglyNumber(self, n: int, a: int, b: int, c: int) -> int:

        def lcm(*args):
            lcm = args[0]
            for i in range(1, len(args)):
                a = lcm
                b = args[i]
                while a % b != 0:
                    a, b = b, a % b
                lcm *= args[i] // b
            return lcm

        def order(num):
            return num // a + num // b + num // c - \
                    num // lcm(a, b) - num // lcm(b, c) - num // lcm (a, c) + \
                    num // lcm(a, b, c)

        l = 0
        r = a * b * c * n

        while r - l > 1:
            mid = l + (r - l) // 2
            if order(mid) < n:
                l = mid
            else:
                r = mid

        return r