There are many such triplets.
Consider any number ending in 4. The next two numbers will end in 5 and 6. The first and last will be divisible by two and the middle one by 5.
To compile a complete list of all such triplets, first draw up a list of all odd numbers that are not prime eg 9, 15, 21 etc. A triplet with that number in the middle will meet your requirements.
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There are no such numbers. The smallest set of three consecutive composite numbers is {8, 9, 10} and the product of these numbers is 720.
8, 9, 10
Basically, composite numbers are the non-prime numbers. Take a table of prime numbers, and look for any two prime numbers, one after the other, that have a difference greater than 2. Any numbers in between are consecutive composite numbers. For example, the next prime number after 13 is 17; that makes 14, 15, and 16 three consecutive non-primes, i.e., composite numbers.
24, 25 and 26 is one possible triplet.
19, 20, 21