The LCM is: 1080

Is that '8' supposed to be a '9'?

1080

Might seem complicated but process will speed up with practice.
To determine the LCM convert each number into prime factors.
27 = 3³
90 = 2 x 3² x 5
12 = 2² x 3
8 = 2³

The LCM is the product of the highest power of each prime factor.
This gives you :-
2³ x 3³ x 5 = 8 x 27 x 5 = 1080.