# Integer LCM

THEOREM    $$\lcm(a, a) = |a|$$

Proof unavailable

THEOREM

One is a left identity element of integer LCM.

$$\forall a \in \mathbb{Z} : \lcm(1, a) = a$$

Proof unavailable

THEOREM

One is a right identity element of integer LCM.

$$\forall a \in \mathbb{Z} : \lcm(a, 1) = a$$

Proof unavailable

THEOREM

The integer $$\lcm$$ function is commutative.

Proof available

THEOREM

The integer $$\lcm$$ function is associative.

Proof available