So there are accepted methods for computing the lowest common multiple given 2 or more numbers.
However I'm been thinking about how to compute/enumerate a set/series of common multiple integers from the lowest common multiple integer to infinity or a limit such as "m < M" (where m is one of the common multiple integers and M is some arbitrary limit set to perhaps 1546).
Is there a an algorithm or formula for this?
The least common multiple of a set of numbers divides every common multiple of those numbers. Proof: if $m$ is the least common multiple and $qm+r$, $0\leq r<m$ is some other common multiple, then $r$ is also a common multiple, thus $r=0$ since $m$ is the least common multiple.
Therefore, given an upper bound $M$, to find all common multiples less than $M$, just find the least common multiple and then list all multiples of that which are less than $M$.