The Number Circle

The numbers 1 through 6 are written in a circle in order, as shown in the figure.
In each step, Lior chooses a number a in the circle whose neighbors are b and c, and replaces
it with the number `(bc)/a`.
Can Lior reach a state where the product of the numbers in the circle is greater than `10^100`
(a) in 100 steps.
(b) in 110 steps