$ab \times ac \times bc = \dfrac{1}{8} \times 3 \times 6$

$a^2 b^2 c^2 = \dfrac{9}{4}$

$(abc)^2 = \dfrac{9}{4}$

$abc = \dfrac{3}{2}$

$\dfrac{abc}{bc} = \dfrac{3/2}{6}$

$a = \dfrac{1}{4}$

$\dfrac{abc}{ac} = \dfrac{3/2}{3}$

$b = \dfrac{1}{2}$

$\dfrac{abc}{ab} = \dfrac{3/2}{1/8}$

$c = 12$

$a + b + c = \dfrac{1}{4} + \dfrac{1}{2} + 12$

$a + b + c = 12.75$ ← *answer*