# The probability distribution of LCM of uniformly distributed integers in {1,…,n}\{1,\ldots,n\}

In the recent paper by Fernandez and Fernandez here on ArXiv, the following formula which was first proved by Diaconis and Erdos appears, on page 2.

For $0 the distribution of the lcm of independent pairs of integers $X_1,X_2$ uniformly drawn from $\{1,\ldots,n\}$ satisfies:

The authors extend these results to $k>2,$ but I am mostly interested in the $k=2$ case.

My Question: What is the implied $t-$dependent constant in the $O_t(\ln n/n)$ term?