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Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?

1. group
2. ring
3. field
4. lattice

ans is lattice .

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How did you draw this lattice? How two elements are related?
I think this lattice has been drawn like this:

For any two elements a and b in this lattice, if a < b then b is the LCM of a and b and a is the GCD of a and b. For example, if 1 and 3 are connected then 3 is the LCM of 1 and 3 and 1 is the GCD of 1 and 3.