Set of Numbers with GCD equal to $1$ Can someone give me a set of $4$ positive integers with $3$ of them having a common divisor that is greater than $1$, but the GCD of all four positive integers is $1$.

If you meant that for any triplet of the positive integers their $\gcd>1$ and the $\gcd$ of all of them is $1$, then the following works:
$$\{2\cdot 3\cdot 5,\:2\cdot 3\cdot 7,\:2\cdot 5\cdot 7,\:3\cdot 5\cdot 7\}$$
