# Revisiting least common multiples for GRE success

Readers of this blog should have noticed a trend by now: many of the GRE math concepts we’ve reviewed are likely straight out of your 9th grade algebra textbook. The straightforward nature of these concepts actually make them even more important to review, as relying on existing knowledge can lull you to sleep on test day (not to mention the points it will cost you on the GRE).

Up for today is the least common multiple, more affectionately known by many as simply the LCM.

## The basics of finding the least common multiple

Questions on the GRE won’t be this simple, but to get us started, let’s find the least common multiple of 12, 15 and 21 by rewriting each number into its prime factors:

*12: 2 x 2 x 3*

*15: 3 x 5*

*21: 3 x 7*

After writing out each number’s prime factors, we take the least number of prime numbers required to ‘build’ each number, and then multiply them together. We do not count the overlaps.

As such, we see that the LCM in this case is 2 x 2 x 3 x 5 x 7 = 420 .

Questions in which you’re asked to find the least common multiple are indicative of the task at hand. In the simplest terms, you’re simply trying to identify the smallest group of prime factors that are required to create the numbers in a given set.

Now that we’ve tackled a simple example, let’s review what a LCM question on the GRE might look like.

## Least common multiples on the GRE

Consider the example below:

*If the least common multiple of two numbers is 45, and one of the numbers is 9, what is the other number?*

*A. 3B. 5C. 7D. 9E. 12*

The wording of this question might seem to be a bit confusing, but let’s break this down in a similar fashion to the example we discussed earlier by simply listing out all the prime factors of 45.

*45: 3 x 3 x 5*

Take a look at the prime factorisation of 45. The question states that the other number is 9, which makes sense now that we see that two of the first three prime factors are 3. That leaves us with 5 as our only remaining factor, and also the answer to our question.

Questions involving least common multiples can seem tricky at times, especially since the people at ETS responsible for writing the GRE do everything they can to create complicated questions from simple concepts. However, applying the basics of how least common multiples work will give you the tools necessary to crack even the toughest questions on the GRE.