Prove that 360 divides (a-2)(a-1)a.a.(a+1)(a+2) there's a question which asks to prove that

360 | a2(a2-1)(a2-4)

I attempted it in the following manner.

a2(a2-1)(a2-4) = (a-2)(a-1)(a)(a+1)(a+2)(a)

The first 5 terms represent the product of 5 consecutive terms. Hence,
One of them will have a factor of 5
One of them will have a factor of 4
One of them will have a factor of 3
One of them will have a factor of 2
=> 5 x 4 x 3 x 2 = 120 will divide the given expression for sure.

Now, how do i bring a factor of 3. I know that i have missed one power of a. But, i think i am missing something. Help will be appreciated

Thank you
Hint: both $(a-2)(a-1)a$ and $a(a+1)(a+2)$ are products of three consecutive integers.
$\;\;\;\;\;\!\!\!\!\!\!\!\!\!\!$