Lowest Common Multiple is Associative

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

Then:


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

where $\lcm$ denotes the lowest common multiple.

Proof
Follows directly from LCM from Prime Decomposition and Max is Associative

Also see

 * Greatest Common Divisor is Associative