A2 With which smallest natural number must we multiply $2^{9} \cdot 3^{14} \cdot 5^{15} \cdot 6^{3}$ to get a perfect square?
(A) 60
(B) 15
(C) 5
(D) 2
(E) 3
A2. Simplify $6^{3}=(2 \cdot 3)^{3}$. This gives us $2^{12} \cdot 3^{17} \cdot 5^{15}$. To get a perfect square, we need to multiply by $3 \cdot 5$, which is 15.