as a,b,c are coprimes to each other

GCD(a,b) = 1 = h

LCM(a,b)=a * b

F(a,b) = 1/(a * b)

now,

F [ 1 / F(a,b) , c ] = HCF [ 1/ab,c] / LCM[1/ab,c]

so, HCF [ 1/ab,c] = 1 / ab

LCM [ 1/ab , c] = c

so required function = 1/ab * 1/c = 1 / abc

and abc = 12....given

a = 1 , b = 3 , c = 4

so, a + b + c = 8