Quantitative Reasoning

Hi guys !

I think I would need your help with prime numbers.

I'm studying with MGMAT. I think I got something wrong about Primes because I am a little bit confused. Here's my problem

135
Primes:3,3,3,5

225
Primes:3,3,5,5

135*125=30375
Primes:3,3,3,3,3,5,5,5 (Let me know if I am wrong but I don't think so)

BUT on MGMAT study guide, on Problem was
J is divisible by 10 and 12 so what is J divisible by:

10
Primes:5,2

12
Primes:3,2,2

So J
Primes 5,2,2,3 + other numbers

Here is the thing I don't understand. MGAMT says that it shouldn't be 5,2,2,2,3 + other numberes because there is one 2 that is redundant.

I got this but then, what is the rule? When do you know that primes can be redundant or not ?
I was thinking maybe because un the first case, where the primes is not redundant, it is because it is a multiplication but when it redundant it is because the problem says J is divisible by 10 "AND" 12.

A little help will be really appreciated! Thanks

Andrew