62 multiplied by 3 is 186
Add on 31 for the half hour
and you get 217
Consider the prime factorization of 20!.

The LCM of 1, 2, ..., 20 must contain all the primes less than 20 in its factorization, so

where
is some integer not divisible by any of these primes.
Compare the factorizations of the remaining divisors of 20!, and check off any whose factorizations are already contained in the product of primes above.
- missing a factor of 2
- ✓
- missing a factor of 2²
- missing a factor of 3
- ✓
- missing a factor of 2
- ✓
- ✓
- missing a factor of 2³
- missing a factor of 3
- missing a factor of 2
From the divisors marked "missing", we add the necessary missing factors to the factorization of
, so that

Then the LCM of 1, 2, 3, …, 20 is


It's pretty easy to go through the choices and none has a[2]=-36 and a[5]=2304. Something's probably wrong with the way the question is typed, but I will answer what's written.



Subtracting,



Answer: a[n] = -816 + 780(n-1) which is none of the above
Check:

