Ring is set with 2 operations such that $(A,+,*)$
1. $(A,+)$ should be an abelian group.
2. $(A,*)$ should be a semigroup.
3. $*$ should be distributed over $+$
Field $(A,+,*)$ :
1. $(A,+)$ should be an abelian group.
2. $(A-{e},*)$ should be an abelian group here $e$ is identity element.
3. $*$ should be distributed over $+$.
Group $(A,LCM):$
1. Associative
2. Should have an identity.
3. Inverse.
In Question $A=\{1,2,3,4,6,8,12,14\}$ and operations are LCM , GCD
(A,LCM) is associative = (a LCM b)LCM c = a LCM (b LCM c)
identity = 1.
but there does not exist Inverse of elements.
so this is not a group. that means it cant be abelian group then it also not be group and field so
Ans: Lattice(D)