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# 1201. Ugly Number III

<https://leetcode.com/problems/ugly-number-iii>

## Description

An **ugly number** is a positive integer that is divisible by `a`, `b`, or `c`.

Given four integers `n`, `a`, `b`, and `c`, return the `nth` **ugly number**.

**Example 1:**

```
**Input:** n = 3, a = 2, b = 3, c = 5
**Output:** 4
**Explanation:** The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3rd is 4.
```

**Example 2:**

```
**Input:** n = 4, a = 2, b = 3, c = 4
**Output:** 6
**Explanation:** The ugly numbers are 2, 3, 4, 6, 8, 9, 10, 12... The 4th is 6.
```

**Example 3:**

```
**Input:** n = 5, a = 2, b = 11, c = 13
**Output:** 10
**Explanation:** The ugly numbers are 2, 4, 6, 8, 10, 11, 12, 13... The 5th is 10.
```

**Example 4:**

```
**Input:** n = 1000000000, a = 2, b = 217983653, c = 336916467
**Output:** 1999999984
```

**Constraints:**

* `1 <= n, a, b, c <= 109`
* `1 <= a * b * c <= 1018`
* It is guaranteed that the result will be in range `[1, 2 * 109]`.

## ac

```java
```