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

Proper supersets