Lowest Common Multiple is Associative

Theorem
Let $a,b,c \in \Z$.

Then $\operatorname{lcm} \{ a, \operatorname{lcm} \{ b , c \} \} = \operatorname{lcm} \{ \operatorname{lcm} \{ a , b \} , c \}$.

Proof
It follows directly from LCM from Prime Decomposition and Max is Associative

Also see

 * Greatest Common Divisor is Associative