\begin{align}

45&= 3 \times 5^2\\

60 &= 2^2 \times 3 \times 5\\

91 &= 7 \times 13\\

105&=3 \times 5 \times 7\\

330 &= 2 \times 3 \times 5 \times 11

\end{align}

Therefore $105$ is the product of three distinct primes.

45&= 3 \times 5^2\\

60 &= 2^2 \times 3 \times 5\\

91 &= 7 \times 13\\

105&=3 \times 5 \times 7\\

330 &= 2 \times 3 \times 5 \times 11

\end{align}

Therefore $105$ is the product of three distinct primes.

*This problem is taken from the UKMT Mathematical Challenges.*