  Pr\"{u}fer domains and subclasses of integral domains such as Dedekind
domains admit characterizations by means of the properties of their ideal
lattices. Interestingly, a Leavitt path algebra $L$, in spite of being
non-commutative and possessing plenty of zero divisors, seems to have its ideal
lattices possess the characterizing properties of these special domains. In [8]
it was shown that the ideals of $L$ satisfy the distributive law, a property of
Pr\"{u}fer domains and that $L$ is a multiplication ring, a property of
Dedekind domains. In this paper, we first show that $L$ satisfies two more
characterizing properties of Pr\"{u}fer domains which are the ideal versions of
two theorems in Elementary Number Theory, namely, for positive integers
$a,b,c$, $\gcd(a,b)\cdot\operatorname{lcm}(a,b)=a\cdot b$ and $a\cdot
\operatorname{gcd}(b,c)=\operatorname{gcd}(ab,ac)$. We also show that $L$
satisfies a characterizing property of almost Dedekind domains in terms of the
ideals whose radicals are prime ideals. Finally, we give necessary and
sufficient conditions under which $L$ satisfies another important
characterizing property of almost Dedekind domains, namely the cancellative
property of its non-zero ideals.
