What do you do if you're looking for least common multiple and all your numbers are prime?

It’s important to remember the distinction between “greatest common factor” and “least common multiple.” A factor of a particular number is a bit like a multiplicative LEGO piece that makes it up; they’re the numbers that other natural numbers can be broken down into by division. A multiple is the opposite; a number and the number that it’s multiplied by (say, 8 x 5) *become factors* of a new number (40, in this case).

When we talk about finding the “least common multiple” of a set of numbers, what we’re asking is this: if you list out multiples of each number, what’s the *first* number in those lists they all have in common? For instance, if we wanted to find the least common multiple between 3 and 5, we could list out their multiples:

3, 6, 9, 12, 15, 18, 21
5, 10, 15, 20, 25, 30

15 is the first multiple that appears in both lists, so the least common multiple of 3 and 5 is 15.