Answer is 540
Step by step
First we find prime factors of each number
(Numbers that when multiplied = the number. This can take some trial and error to find these numbers)
90 = 2 × 3 × 3 × 5
108 = 2 × 2 × 3 × 3 × 3
Now we multiply each number the most times it shows up in either factorization
(2) 2’s, (3) 3’s and (1) 5
2 x 2 x 3 x 3 x 3 x 5 = 540
Problem solved