Let a=25⋅33⋅72a = 2^5 \cdot 3^3 \cdot 7^2a=25⋅33⋅72 and b=23⋅34⋅5b = 2^3 \cdot 3^4 \cdot 5b=23⋅34⋅5. What is gcd(a,b)\gcd(a, b)gcd(a,b)?
23⋅33⋅5=10802^3 \cdot 3^3 \cdot 5 = 108023⋅33⋅5=1080
23⋅33=2162^3 \cdot 3^3 = 21623⋅33=216
25⋅34⋅5⋅72=1008002^5 \cdot 3^4 \cdot 5 \cdot 7^2 = 10080025⋅34⋅5⋅72=100800
23⋅33⋅72=15122^3 \cdot 3^3 \cdot 7^2 = 151223⋅33⋅72=1512