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