For $ 3 $: $ \min(2, 4) = 2 $
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- Question: What is the greatest common divisor of $ 2^5 \cdot 3^2 \cdot 5 $ and $ 2^3 \cdot 3^4 \cdot 7 $?
- Solution: To find the GCD, take the minimum exponent for each common prime factor:
- For $ 2 $: $ \min(5, 3) = 3 $
- $ 5 $ and $ 7 $ are not common to both.
- Thus, the GCD is $ 2^3 \cdot 3^2 = 8 \cdot 9 = 72 $.
- The greatest common divisor is $ \boxed{72} $.
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