Question

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

Answer 1

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.