Lowest Common Multiple is Associative

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

Then:


 * $\operatorname{lcm} \left\{ a, \operatorname{lcm} \left\{ b , c \right\} \right\} = \operatorname{lcm} \left\{ \operatorname{lcm} \left\{ a , b \right\} , c \right\}$

where $\operatorname{lcm}$ denotes the lowest common multiple.

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

Also see

 * Greatest Common Divisor is Associative