# Longest Rubik's cube algorithm - maximization problem

For a given Rubik's cube algorithm $$A$$ let $$\mathfrak C(A)$$ be the number of times, we have to repeat algorithm $$A$$ to get back to where we've started. For example if $$A=RUR'U'$$ then $$\mathfrak C(A)=6$$ The question is:
What is the greatest value of $$\mathfrak C(A)$$, we can achieve?
This question is equivalent to following maximization problem:
Maximize $$LCM(a_1,a_2,...a_i,b_1,b_2,...b_j)$$ under the following conditions: $$~a_1,a_2,...a_i,b_1,b_2,...,b_j \in \mathbb N_+~$$ $$a_1+a_2+...+a_i=8$$ $$b_1+b_2+...+b_j=12$$ $$2 \ | \ (a_1+a_2+...+a_i+b_1+b_2+...+b_j)$$ Where LCM is Least Common Multiple function.
Thanks for all the help.

Wikipedia's article on the Rubik's cube group says that the largest order of any element in the group is 1260. For instance, $$RU^2D'BD'$$ is one such move.