The highest number of elements in set.

[fidanym]

Hello, I am new to these forums and I have a math problem I can't figure out. The text is in other language so I will try my best at translating it to English.


"We can say a set of natural numbers is closed if for every 2 elements a and b it contains the lowest common denominator (LCD) (in other words the smallest natural number that divides with both a and b).
For the set CA we will say it is the closure of A if it is the smallest closed set so that A is the subset of CA. What is the biggest number of elements that CA can have if |A|=n?"


I've failed to even find a way to start solving this.
Does this make any sense? If yes please help me solve it, thanks

 

[pka]

"We can say a set of natural numbers is closed if for every 2 elements a and b it contains the lowest common denominator (LCD) (in other words the smallest natural number that divides with both a and b).
For the set CA we will say it is the closure of A if it is the smallest closed set so that A is the subset of CA. What is the biggest number of elements that CA can have if |A|=n?"

I am not sure that you translated it correctly. Particularly: "in other words the smallest natural number that divides with both a and b"

The GCD(3,9)=3 BUT the smallest natural number that divides with both 3 and 9 is 1.
So 1 be all a set needs to be closed. I don't think that is what you mean.

Usually we consider LCM or GCD.

 

[fidanym]

Yeah that correction is true but it's not asking for the exact number, it's asking for the maximum amount of numbers that this set is true for and I think it should be solved by ∀x and ∃x as it's a part of a Discrete Mathematics class I'm taking