| A lot of research has been made on the logarithm of the least com-mon multiple of sets of integers. For example, J. Cilleruelo, J. Rue, P. Sarka and A. Zumalacdrregui proved that for almost every set A (?)1,2,…,n}. They also proved that for any0<θ<1, for almost all sets A (?)1,2,…, n} of size [nθ]. In this paper we generalize their results. Let be an arithmetic progression with u>0, d>0and (u, d)=1.We study the logarithm of the least common multiple of subsets of U by using the probabilistic methods.We show that for any0<θ<1, for almost all sets A (?) U of size [nθ]. |
