Start with a set of a few distinct natural numbers.

For any 2 members, add their least common multiple to the set, if and only if it was not already in the set.

Continue the task until it cannot be done.

Call the result a final list.

Examples:

a. (2,4,8,16) a is a final list.

b. (2,3,4,6) will become a final list once we add number 12 to the set.

What can be the longest final list, if the initial set had 10 distinct numbers?

2^10 - 1.

For instance, if the initial set had 10 primes, then the full set is the set of all products of the numbers in any non-empty subset of the 10 primes.

In general, n primes lead to a full set of 2^n - 1.

For instance, {2,3,5} generates a final set of {2,3,5,6,10,15,30}

/*********************************************/

Edited to reflect Ady's preferred wording

*Edited on ***January 28, 2018, 6:58 pm**