Lowest Common Multiple is Associative

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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