AllButOneDivisor | Topcoder Archive

Problem Statement

You are given a int[] divisors containing K elements. Find a positive integer n such that exactly K-1 elements of divisors are exact divisors of n. If there are several such numbers n, return the smallest possible one. If no such number n exists, return -1 instead.

Definition

Class:: AllButOneDivisor
Method:: getMinimum
Parameters:: int[]
Returns:: int
Method signature:: int getMinimum(int[] divisors)
(be sure your method is public)

Notes

A number x is an exact divisor of y if y divided by x yields an integer result.
If x is an exact divisor of y then we call y a multiple of x.

Constraints

divisors will contain between 2 and 6 elements, inclusive.
Each element of divisors will be distinct.
Each element of divisors will be between 1 and 15, inclusive.

Examples

```
{2,3,5}
```
```
Returns: 6
```
There are many possible values for n in this case. For example: 6, 15, 75 and 12. 6 is the smallest of them.
```
{2,4,3,9}
```
```
Returns: 12
```
```
{3,2,6}
```
```
Returns: -1
```
Every multiple of 3 and 2 is also a multiple of 6. Every multiple of 6 is also a multiple of 2 and 3. Therefore, a number that is a multiple of exactly 2 out of the three elements in this array cannot exist.
```
{6,7,8,9,10}
```
```
Returns: 360
```
```
{10,6,15}
```
```
Returns: -1
```

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