LCM from Prime Decomposition

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

From Expression for Integers as Powers of Same Primes, let:

That is, the primes given in these prime decompositions may be divisors of either of the numbers $a$ or $b$.

Then:


 * $\lcm \set {a, b} = p_1^{\max \set {k_1, l_1} } p_2^{\max \set {k_2, l_2} } \ldots p_r^{\max \set {k_r, l_r} }$

where $\lcm \set {a, b}$ denotes the lowest common multiple of $a$ and $b$.

Also see

 * GCD from Prime Decomposition