jmc

Suppose the 3 different prime factors are $a$, $b$, and $c$. The prime powers in the prime factorization of a perfect square must have even exponents. Since the square must be as small as possible, we let the exponents all be 2, so the prime factorization is $a^2{b}^2{c}^2$. We make the square as small as possible by letting the three primes be 2, 3, and 5, so we have $$a^2{b}^2{c}^2=2^2\cdot 3^2\cdot 5^2=(2\cdot 3\cdot 5{)}^2=30^2=\boxed{900}.$$