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.
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.
The sum is 84 and the GCF is 6
3 (21+5)
The Greatest Common Factor is 3
2(24 + 7)
The sum is: 5+1 = 6
The GCF is 7.
GCF = 4, sum = 84.
They are: GCF = 5 and LCM = 325 and the sum is 5+325 = 330
The sum is 335.
The sum is 84 and the GCF is 6
9(2 + 3)
3 (21+5)
11(5 + 6)
5(8 + 5)
9(2 + 3)
7(7 + 9)
This question requires more information in order for it to make any sense at all! You cannot have a sum of a number: you need two or more numbers. A single number cannot have a GCF. The GCF needs to be COMMON to two or more numbers.