LCM of 3 Integers in terms of GCDs of Pairs of those Integers

Theorem
Let $a, b, c \in \Z_{>0}$ be strictly positive integers.

Then:
 * $\lcm \set {a, b, c} = \dfrac {a b c \gcd \set {a, b, c} } {d_1 d_2 d_3}$

where:
 * $\gcd$ denotes greatest common divisor


 * $\lcm$ denotes lowest common multiple


 * $d_1 = \gcd \set {a, b}$


 * $d_2 = \gcd \set {b, c}$


 * $d_3 = \gcd \set {a, c}$