LCM (noch nicht übersetzt)

Problem 858

Define G(N)=Slcm(S) where S ranges through all subsets of {1,,N} and lcm denotes the lowest common multiple. Note that the lcm of the empty set is 1.

You are given G(5)=528 and G(20)=8463108648960.

Find G(800). Give your answer modulo 109+7.