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What is a factor? What is a multiple?

Greatest Common Factors and Least Common Multiples

What is a factor? What is a multiple?

Have you ever had a box of chocolates, and you tell yourself that you'll just have each day? That way, if there are 12 chocolates, you can make them last days πŸ˜‹.
But, self-control is hard, so maybe instead you'll have a day and make them last days. Or, honestly, just have in day. Tomorrow's a new day β˜€οΈ.

These are factor pairs! We can get to 12 in three different ways:

So, the factors of 12 are .
On the other hand, if we wanted to buy more boxes of chocolates, we could buy 1 box ( chocolates), 2 boxes ( chocolates), 3 boxes ( chocolates), and so on.
So, the multiples of 12 are

Notice, we can keep adding 12 to get more multiples, but we can't get more factors. To remember the difference, just think more multiples and few factors!

GCF & LCM Calculator

What is the

of

and

?

Use the

We're looking for the smallest multiple that these two numbers share. Think of it as a race! 🐒 πŸ‡

Click the β€œStart” button below to start generating multiples for each number. When you see a common multiple - a number that appears on both sides - click "Stop."

🏁
🏁

The LCM is

Not quite, look for the multiple that appears in both tables - hint: it's green!

That's right! Our LCM is πŸ”₯!

We can use the formula below ⬇️ to calculate LCM.

Step 1: Find the GCF

From our formula, we can see that we need the GCF, or greatest common factor, of our two numbers. So let's get that first.

To find the GCF, we need to find the factors of and .

We need the greatest common factor, so select the matching factor between the two numbers that is the BIGGEST.

πŸš— πŸš—

πŸš— πŸš—

Step 2: Plug-In the Formula

That's right! Our GCF is . So, we have everything we need for our formula now - plug everything in below ⬇️

That's right! When you're ready, click the πŸ† below to get the final, calculated LCM.

Step 3: Calculate

When we do the math, we find that our LCM is:

Let's start by getting all the factors of each of our numbers. We'll use the U-Turn method to find the pairs of factors.

πŸš— πŸš—

πŸš— πŸš—

Now, pick the BIGGEST factor that both numbers have in common.

That's right! Our greatest common factor, or GCF, is .

Recap 🧒 GCF & LCM

Remember, GCF stands for Greatest Common Factor. Follow these steps to find the GCF of two numbers:

Step 1: Get All Factor Pairs

First, find all the factors for both your numbers.

Step 2: Find the Greatest Common Factor

Now, find the biggest factor that both numbers have in common - that's your GCF!

Remember, LCM stands for Least Common Multiple. One way to find the LCM of two numbers is to just list out multiples:

Step 1: List out Multiples

List out the multiples of each number, alternating one for each number.

Step 2: Stop πŸ›‘

Stop as soon as you see a multiple in common between your two numbers - that's the LCM!

Remember, LCM stands for Least Common Multiple. One way to find the LCM of two numbers is to use a formula:

Step 1: Get the GCF

First, you'll need the GCF of the two numbers. List out the factors for both numbers, and find the biggest factor they have in common.

Step 2: Plug into the Formula πŸ›‘

Plug everything into this formula:

Calculate it out to get your LCM!

No sweat if this doesn't all make sense yet. Click below for more help!

What is a factor?

Let’s say we decide to host a Mardi Gras partyβ€”on a budget. πŸ’œπŸ’šπŸ’›

We can use factors to plan out how many people we can invite, based on the amount of food we have:

24 slices of king cake πŸ‘‘

18 servings of jambalaya 🍽️

If we want everyone to get an equal number of king cake slices and an equal amount of jambalaya, what’s the maximum number of guests we can invite?

To answer this question, we need to use factors.

Factors are the pairs of numbers that multiply to form a given number: for example, the factors of 24 are 1 & 24, 2 & 12, 3 & 8, and 6 & 4.

What are the factors of 18? Select the matching factor pairs:

We need the number of guests to be a factor of both 24 and 18. And, if we want the most guests we can have, we want the largest factor they share.

Here’s a Venn diagram of the factors for 18 and 24. Click on the largest one they have in common:

18

24

6 is the Greatest Common Factor (GCF)β€”AKA, the largest factor two numbers have in common - of 18 and 24.

But, using a Venn diagram isn’t the fastest way to find the GCF. Keep scrolling to try out our favorite method: the U-Turn Method!

How do you calculate the GCF?

The U-Turn Method is a trick we can use to get all the factors. So, channel your inner Olivia Rodrigoβ€”let’s get our GCF driver’s license!

Let’s find the greatest common factor of 12 and 30.

We’ll fill in each row of the tables below with a factor pair: starting with 1 on the left side, which goes into times, and times.

πŸš— 12 πŸš—

1
12
2
6
3
4
4
3

↩️

πŸš— 30 πŸš—

1
30
2
15
3
10
5
6
6
5

↩️

Nice work! So to find our greatest common factor, or GCF, we need to find all our factors, then identify the common factors, and then find the largest one.

A Guide to Multiples

Multiples are what we get after we multiply a number by an integer (not a fraction): for example, the multiples of 3 are 3, 6, 9, 12, 15, and so on!

Try entering in the first five multiples of 6:

You can use multiples to find the Least Common Multiple (LCM), which is the smallest multiple two numbers have in common.

Let's say we're making some Mardi Gras necklaces with different color beads for our party.

At the store, green beads are sold in packs of 8, and purple beads in packs of 12. We can find the least common multiple of 8 and 12 to figure out the fewest number of packs we need to buy to have an equal number of green and purple beads.

That’s not the only method you can use to find the LCM, though. You can actually use the GCF of two numbers to calculate the LCM of those numbers (let’s call them a and b) using this formula:

This formula looks complicated, but it’s actually not so bad! To find the LCM, all you have to do is multiply the two numbers together, and divide them by their GCF.

Let’s try it out with our same example numbers: 8 and 12. The greatest common factor of 8 and 12, which we can find using the U-Turn method, is 4:

πŸš— 8 πŸš—

1
8
2
4

↩️

πŸš— 12 πŸš—

1
12
2
6
3
4

↩️

We can plug that into our formula like so:

Click the πŸ† when you’re ready to see the simplified answer!

With this method, we land on the same answer: the least common multiple of 8 and 12 is 24!

Nice work mastering LCM and GCF!