\(\text{$15=3\cdot 5$ so $15n$ being a perfect square means $n=15 k^2$}\\ \text{We want all of these up to 1000}\\ 15k^2 \leq 1000\\ k^2 \leq 66\frac 2 3\\ k\leq 8\\ \text{So we have $n = 15,60, 135, 240,375,540,735,960$}\)
\(\text{$15=3\cdot 5$ so $15n$ being a perfect square means $n=15 k^2$}\\ \text{We want all of these up to 1000}\\ 15k^2 \leq 1000\\ k^2 \leq 66\frac 2 3\\ k\leq 8\\ \text{So we have $n = 15,60, 135, 240,375,540,735,960$}\)
