What multiples do 15 and 18 have in common?

Are you on the hunt for the GCF of 15 and 18? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!

Want to quickly learn or show students how to find the GCF of two or more numbers? Play this very quick and fun video now!

First off, if you're in a rush, here's the answer to the question "what is the GCF of 15 and 18?":

GCF of 15 and 18 = 3

What is the Greatest Common Factor?

Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:

• Greatest Common Denominator (GCD)
• Highest Common Factor (HCF)
• Greatest Common Divisor (GCD)

There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.

For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them.

For 15 and 18 those factors look like this:

• Factors for 15: 1, 3, 5, and 15
• Factors for 18: 1, 2, 3, 6, 9, and 18

As you can see when you list out the factors of each number, 3 is the greatest number that 15 and 18 divides into.

Prime Factors

As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.

List out all of the prime factors for each number:

• Prime Factors for 15: 3 and 5
• Prime Factors for 18: 2, 3, and 3

Now that we have the list of prime factors, we need to find any which are common for each number.

In this case, there is only one common prime factor, 3. Since there are no others, the greatest common factor is this prime factor:

GCF = 3

Find the GCF Using Euclid's Algorithm

The final method for calculating the GCF of 15 and 18 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.

If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page.

Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. Grab a pencil and paper and give it a try for yourself. (or just use our GCD calculator - we won't tell anyone!)

Cite, Link, or Reference This Page

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• <a href="//visualfractions.com/calculator/greatest-common-factor/gcf-of-15-and-18/">Greatest Common Factor of 15 and 18</a>

• "Greatest Common Factor of 15 and 18". VisualFractions.com. Accessed on September 6, 2022. //visualfractions.com/calculator/greatest-common-factor/gcf-of-15-and-18/.

• "Greatest Common Factor of 15 and 18". VisualFractions.com, //visualfractions.com/calculator/greatest-common-factor/gcf-of-15-and-18/. Accessed 6 September, 2022.

• Greatest Common Factor of 15 and 18. VisualFractions.com. Retrieved from //visualfractions.com/calculator/greatest-common-factor/gcf-of-15-and-18/.

The LCM of 15 and 18 is 90.

Steps to find LCM

1. Find the prime factorization of 15
   15 = 3 × 5
2. Find the prime factorization of 18
   18 = 2 × 3 × 3
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 2 × 3 × 3 × 5

4. LCM = 90

MathStep (Works offline)

Find least common multiple (LCM) of: 30 & 36 45 & 54 5 & 6 75 & 90 105 & 126 30 & 18 15 & 36 45 & 18 15 & 54 75 & 18 15 & 90 105 & 18 15 & 126

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

Use the form below to do your conversion, Convert Number to factors, separate numbers by comma and find factors of a number.

We get factors of 15,18 numbers by finding numbers that can divide 15,18 without remainder or alternatively numbers that can multiply together to equal the target number being converted.

In considering numbers than can divide 15,18 without remainders. So we start with 1, then check 2,3,4,5,6,7,8,9, etc and 15,18

Getting factors is done by dividing 15,18 with numbers lower to it in value to find the one that will not leave remainder. Numbers that divide without remainders are the factors.

Factors are whole numbers or integers that are multiplied together to produce a given number. The integers or whole numbers multiplied are factors of the given number. If x multiplied by y = z then x and y are factors of z.

if for instance you want to find the factors of 20. You will have to find combination of numbers that when it is multiplied together will give 20. Example here is 5 and 4 because when you multiplied them, it will give you 20. so they are factors of the given number 20. Also 1 and 20, 2 and 10 are factors of 20 because 1 x 20 = 20 and 2 x 10 = 20. The factors of the given interger number 20 are 1, 2, 4, 5, 10, 20

To calculate factors using this tool, you will enter positive integers, because the calculator will only allow positive values, to calculate factors of a number. if you need to calculate negative numbers, you enter the positive value, get the factors and duplicate the answer yourself with all the give positive factors as negatives like as -5 and -6 as factors of number 30. On the other hand this calculator will give you both negative factors and positive integers for numbers. For instance, -2 , -3,-4 etc.

factors is like division in maths, because it gives all numbers that divide evenly into a number with no remainder. example is number 8. it is is evenly divisible by 2 and 4, which means that both 2 and 4 are factors of number 10.

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