Limit theorems for the least common multiple of random integer sets

In my talk I shall consider two models for random integer sets and derive limit theorems for the least common multiple of their elements. In the first model a random set is defined by the Bernoulli sieving of $\{1,2,\ldots,n\}$ with a constant rate $\theta\in(0,1)$. In the second model the set consists of k independent uniform random variables on $\{1,2,3,\ldots,n\}$.