  This thesis is devoted to studying estimates of the least common multiple of
some integer sequences. Our study focuses on effective bounding of the
$\mathrm{lcm}$ of some class of quadratic sequences, as well as arithmetic
progressions and strong divisibility sequences. First, we have used methods of
commutative algebra and complex analysis to establish new nontrivial lower
bounds for the $\mathrm{lcm}$ of some quadratic sequences. Next, a more
profound study of the arithmetic properties of strong divisibility sequences
allowed us to obtain three interesting identities involving the $\mathrm{lcm}$
of these sequences, which generalizes some previous identities of Farhi (2009)
and Nair (1982); as consequences, we have deduced a precise estimates for the
$\mathrm{lcm}$ of generalized Fibonacci sequence (the so-called Lucas
sequences). We have also developed a method that provides an effective version
to the asymptotic result of Bateman (2002) concerning the $\mathrm{lcm}$ of an
arithmetic progression. Finally, we found that the latter method can be adapted
to estimate the $\mathrm{lcm}$ of the sequence $(n^2+1)_n$, which allowed us in
particular to improve the lower bounds of Farhi (2005) and Oon (2013). The
thesis also includes a general presentation of some literature results.
