Let [a,b] be the LCM of a and b, and (a,b) be the GCD of a and b.

Since (a,b) = 8, [a,b] = 96, then a ×

 b = [a,b] × (a,b) = 96 ×

 8 = 768.

As (a,b) = 8, let a = 8m, b = 8n, in which (m,n) = 1.

=> a ×

 b = 8m × 8n = 768. Thus, m × n = 768 ÷ (8 ×

 8) = 12.

(m,n) = 1, so all the pairs (m;n) which have GCD = 1 and m ×

 n = 12 are:

(1;12),(3;4),(4;3),(12;1).

=> (a;b) = (8;96),(24;32),(32;24),(96;8).

Therefore, there are 2 possible values of a + b: 8+ 96 = 104, 24 + 32 = 56.

Answer. 104 and 56

Let [a,b] be the LCM of a and b, and (a,b) be the GCD of a and b.

Since (a,b) = 8, [a,b] = 96, then a \(\times\) b = [a,b] \(\times\) (a,b) = 96 \(\times\) 8 = 768.

As (a,b) = 8, let a = 8m, b = 8n, in which (m,n) = 1.

=> a \(\times\) b = 8m \(\times\) 8n = 768. Thus, m \(\times\) n = 768 \(\div\) (8 \(\times\) 8) = 12.

(m,n) = 1, so all the pairs (m;n) which have GCD = 1 and m \(\times\) n = 12 are:

(1;12),(3;4),(4;3),(12;1).

=> (a;b) = (8;96),(24;32),(32;24),(96;8).

Therefore, there are 2 possible values of a + b: 8+ 96 = 104, 24 + 32 = 56.

Answer. 104 and 56