jmc

We use the fact that a number which is divisible by three primes must be divisible by their product -- this comes from the Fundamental Theorem of Arithmetic. Since we are looking for the least positive integer, we look at the three smallest primes: 2, 3, and 5. Multiplying these yields $2\times 3\times 5=\boxed{30}$, which is the least positive integer divisible by three distinct primes.