Solution
= Solution
Prime exponents must obey simultaneous congruences modulo $2,3,5$. The choices
$$
v_2(n)=15,\qquad v_3(n)=10,\qquad v_5(n)=6
$$
satisfy the required congruences. Thus one example is
$$
\boxed{n=2^{15}3^{10}5^6.}
$$
= Solution
Prime exponents must obey simultaneous congruences modulo $2,3,5$. The choices
$$
v_2(n)=15,\qquad v_3(n)=10,\qquad v_5(n)=6
$$
satisfy the required congruences. Thus one example is
$$
\boxed{n=2^{15}3^{10}5^6.}
$$