ugly-number-iii

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Algorithms

An ugly number is a positive integer that is divisible by <code>a</code>, <code>b</code>, or <code>c</code>.

Given four integers <code>n</code>, <code>a</code>, <code>b</code>, and <code>c</code>, return the <code>nth</code> ugly number.

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

<pre>
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.
</pre>

Example 3:

<pre>
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.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n, a, b, c &lt;= 109</code></li>
	<li><code>1 &lt;= a * b * c &lt;= 1018</code></li>
	<li>It is guaranteed that the result will be in range <code>[1, 2 * 109]</code>.</li>
</ul>