Non-zero multiples of 8: 1 x 8 = 8 2 x 8 = 16 3 x 8 = 24 4 x 8 = 32 5 x 8 = 40 etc.
Non-zero multiples of 12: 1 x 12 = 12 2 x 12 = 24 3 x 12 = 36 4 x 12 = 48 etc.
Plot the multiples on two parallel number lines. You'll see that 24 is the first place where they share a multiple. That's the "least common multiple" of those two numbers.