1.1. How many solutions in natural numbers does the equation $\operatorname{LCM}(n, k)=2^{3} 3^{5} 5^{7}$ have?
1.1. If $n=2^{a} 3^{b} 5^{c}, k=2^{A} 3^{B} 5^{C}$, then the pair $(a, A)$ can take 7 values (one of the numbers is 3, the other is from 0 to 3), the pair $(b, B)-11$ values, $(c, C)-15$ values. Thus, the answer is $7 \cdot 11 \cdot 15=1155$.