Juan rolls a fair regular octahedral die marked with the numbers $1$ through $8$. Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of $3$? The original answer is in the form of \frac{k}{m}, where the fraction is in simplest form. Please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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