Multiplying, we see that $6_8 \cdot 7_8 = 42_{10} = 52_8.$ Written out, $$\begin{array}{@{}c@{\;}c@{}c@{}c} && & 6_8 \\ & \times & & 7_8 \\ \cline{2-4} & & 5 & 2_8 \\ \end{array} $$ Thus, the answer is $\boxed{52_8}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the product of $6_8 \cdot 7_8.$ Express your answer in base $8.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
52_8
Find the product of $6_8 \cdot 7_8.$ Express your answer in base $8.$
test