Given a=23⋅32⋅5a = 2^3 \cdot 3^2 \cdot 5a=23⋅32⋅5 and b=22⋅3⋅7b = 2^2 \cdot 3 \cdot 7b=22⋅3⋅7, find lcm(a,b)\text{lcm}(a, b)lcm(a,b).
2⋅3⋅5⋅72 \cdot 3 \cdot 5 \cdot 72⋅3⋅5⋅7
23⋅32⋅5⋅72^3 \cdot 3^2 \cdot 5 \cdot 723⋅32⋅5⋅7
23⋅32⋅52⋅72^3 \cdot 3^2 \cdot 5^2 \cdot 723⋅32⋅52⋅7
25⋅33⋅5⋅72^5 \cdot 3^3 \cdot 5 \cdot 725⋅33⋅5⋅7