For a Boolean Algebra with 2 operators, there must be 2 identity elements, one for each of the operators.
And as per definition, identity element is such an element that any elements operated with that element would produce the element itself i.e. a∗e=a where a is the element and e is the identity element.
So when operator is LCM , then the LCM of 1 with any of the given elements would result in that element i.e. LCM(1,30)=30 ; LCM(1,5)=5 etc for all the elements
When operator is HCF , the HCF of 30 with any other element would produce the same element i.e. HCF(2,30)=2; HCF(6,30)=6 etc for all the elements.
Hence the identity elements for the given Boolean Algebra would be 1 and 30 .