How do you get the sum of a gcf?

Answer 1

You cannot.

LCM{2,6,12} = 12 and GCF{2,6,12} = 2

LCM{4,6,12} = 12 and GCF{4,6,12} = 2

The two sets have the same LCM and GCF but, clearly, their sums are different.

Answer 2

Given any set of numbers, there is only one GCF for them. The sum of that single number will be itself so there is really not much to the sum: it is the GCF.