Lowest Common Multiple is Associative

Theorem

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

Then:

$\lcm \set {a, \lcm \set {b, c} } = \lcm \set {\lcm \set {a, b}, c}$

where $\lcm$ denotes the lowest common multiple.

Proof

Follows directly from LCM from Prime Decomposition and Max Operation is Associative.

Also see

• Greatest Common Divisor is Associative