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.


Solution
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