Well, today, we’re walk to learn the one technique that it s okay you the answers come both really easily.

You are watching: How are a common denominator and a common multiple alike and different

Let’s go!

But first let’s testimonial the straightforward definitions the each.

## What Is GCF and also LCM

The Greatest common Factor (also well-known as GCF) is the largest number the divides evenly right into each number in a given set of numbers.

The Least usual Multiple (also recognized as LCM) is the smallest confident multiple that is common to two or much more numbers.

## Why execute You need Both Methods

So will certainly there ever before be a time once we will need to use both the GCF, Greatest common Factor and LCM, Least usual Multiple?

Yes, whenever we do operations with fractions!

For instance, we might need to use the LCM to help us add two fractions, and additionally the GCF to simplify our result.

Consequently, you will need to know how to use both that these techniques at the same time.

## How To discover GCF and LCM

How perform you keep them straight and also not mix them up?

Great question!

First, at any time you room asked to discover both the greatest common factor and also the least usual multiple, always choose the prime administrate method, or the listing of prime factors, as it will save you time and also is the only method that will job-related consistently.

And secondly, usage the last letter of GCF and also LCM to find what you need!

Here’s a trick: GCF = Fewer and also LCM = More

Remember, once using our element factorization technique, we pick the fewest usual factors for the GCF, and for the LCM, we select the most of each factor as discussed at Minnesota State University.

### Example #1 — two Numbers

Working a few problems will aid to make sense of exactly how this works.

For our very first question, let’s uncover the GCF and also find the LCM of 2 numbers: 12 and also 18

Find GCF and also LCM of two Numbers — Example

This way that the GCF the (12 and 18) is 6, and the LCM of (12 and also 18) is 36.

### Example #2 — 3 Numbers

Now let’s job-related a difficulty involving 3 numbers.

Find the GCF and also LCM of 15, 18, 24

Find GCF and also LCM of three Numbers — Example

So…

The GCF the (15, 18, and 24) is 3.And the LCM of (15, 18, and also 24) is 360.

Using prime factorization and also our trick for remembering what determinants to pick is a snap!

## Closing Thoughts

Now, ns would favor to suggest out that the expression GCF has plenty of synonyms. So, if you ever before hear or see among these alternative phrases, nothing be alarmed. Just know castle all average the exact same thing – find the best positive integer that divides evenly into two or an ext numbers.

The alternate terminologies for the Greatest typical Factor (GCF) are:

Highest common Factor (HCF)Greatest common Divisor (GCD)Greatest typical Measure (GCM)Highest common Divisor (HCD)

And when there are no alternating terminologies because that Least usual Multiple, you will certainly hear Least common Multiple (LCM) and Least usual Divisor (LCD) provided together fairly often. Sometimes, they will certainly be supplied interchangeably.

The LCM is how we find common multiples of 2 or much more numbers, conversely, the LCD is the least typical multiple in a fraction’s denominator. So, the LCD is a subset or special situation of the LCM. Yet in every honesty, they require the exact same math process, so many teachers and students usage these 2 phrases as synonyms.

But, nevertheless of what the an approach is called, the procedure for finding the greatest common factor and the least typical multiple is really straightforward.

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## Worksheet (PDF) — Hands on Practice

Put the pencil to file in these easy to follow worksheets — expand your knowledge!

GCF and LCM — Practice difficulties GCF and LCM — Step-by-Step solutions

## Video indict — full Lesson w/ thorough Examples

Together us will occupational through assorted exercises involving two and also three numbers to master the techniques of detect the GCF and LCM and never obtaining them combined up.

30 min

Introduction to Video: GCF and also LCM00:00:26 – how do you uncover the Greatest common Factor and also the Least common Multiple?00:01:45 – uncover both the GCF and LCM (Examples #1-3)00:14:17 – identify the GCF and the LCM of three numbers (Examples #4-7)Practice Problems through Step-by-Step solutions Chapter Tests with video clip Solutions