In this paper we find a formula for the Alexander polynomial
${{\Delta }_{p1,...,{{p}_{k}}\left( x \right)}}$
of pretzel knots and links with
$\left( {{p}_{1}},...,{{p}_{k}},-1 \right)$
twists, where
$k$
is odd and
${{p}_{1}},...,{{p}_{k}}$
are positive integers. The polynomial
${{\Delta }_{2,3,7}}\left( x \right)$
is the well-known Lehmer polynomial, which is conjectured to have the smallest Mahler measure among all monic integer polynomials. We confirm that
${{\Delta }_{2,3,7}}\left( x \right)$
has the smallest Mahler measure among the polynomials arising as
${{\Delta }_{p1,...,{{p}_{k}}\left( x \right)}}$
.