## Greatest Common Divisors

1. Find a set of four positive integers, such that the greatest common divisor (GCD) of each pair of integers is a unique number. (There are six different pairs.)
2. Find a set of four positive integers, such that the GCD of each subset of three integers is a unique number.
3. Find a set of five positive integers, such that the GCD of each pair of integers is a unique number.
4. Find a set of five positive integers, such that the GCD of each subset of three integers is a unique number.
5. Find a set of five positive integers, such that the GCD of each subset of four integers is a unique number.
Repeat the above with the requirement that each GCD found must be greater than 1.
In each case, try to find the set with the smallest sum.

Source: Original.

Solutions were received from Joseph DeVincentis, Le Ba Nguyen, and Alan Zimmermann, Luc Kumps, Philippe Fondanaiche. All were unique. Al Zimmermann's solutions follow:
```1.  (4, 9, 12, 18)
2.  (6, 10, 15, 30)
3.  (8, 24, 27, 36, 54)
4.  (20, 45, 60, 90, 108)
5.  (30, 42, 70, 105, 210)

> Repeat the above with the requirement that each GCD
> found must be greater than 1.

1.  (6, 10, 15, 30)
2.  (12, 20, 30, 60)
3.  (12, 20, 45, 60, 90)
4.  (30, 42, 70, 105, 210)
5.  (60, 84, 140, 210, 420)
```

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