MathDB

A four-element set

\{a, b, c, d\}

of positive integers is called good if there are two of them such that their product is a mutiple of the greatest common divisor of the remaining two. For example, the set

\{2, 4, 6, 8\}

is good since the greatest common divisor of

2

and

6

2

, and it divides

4\times 8=32

.
Find the greatest possible value of

n

, such that any four-element set with elements less than or equal to

n

is good.
Proposed by Victor and Isaías de la Fuente

5

Problems(1)