Least Common Multiple Worksheets

On this page we have worksheets for finding the least common multiple of 2 or 3 numbers.

We also have a link to our Least Common Multiple Calculator which will quickly and easily find the lowest common multiple between 2 or more numbers, and also show you the working out along the way.

Using these least common multiple worksheets will help your child to:

• understand what the leqast common multiple is;
• find the least common multiple between two or three numbers.

First of all let us think about what a multiple is.

A multiple is a number which can be divided by another number with no remainder.

It can also be thought of as the result of a product between two numbers.

In other words, any number belonging to any times table is a multiple of that times table.

• 3, 6, 9, 12, 15, 18, ... are all multiples of 3 because they are in the 3 times table
• 10, 20, 30, 40 , 50, ... are all multiples of 10 because they are all in the 10 times table.
• 3 x 4 = 12, so 12 is a multiple of both 3 and 4.
• 5 x 5 = 25 so 25 is a multiple of 5
• 12 x 5, so 60 is a multiple of both 5 and 12.

Now a common multiple is a multiple that several numbers have in common.

And the Least Common Multiple between two numbers is the smallest number that is a multiple of both numbers.

And the Least Common Multiple between lots of numbers, is the smallest multiple that all the numbers have in common.

The Least Common Multiple is the same as the Lowest Common Multiple.

It is often abbreviated to the LCM.

You can always find a common multiple of two numbers by multiplying them together, but this may not always be the least common multiple (as there may be a smaller common multiple).

Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.

It will also show you the working out using a choice of two different methods.

There are also some worked examples on the page with explanation of how it works.

So how can we find the greatest common multiple?

There are a number of different ways to do this, but our worksheets use two of the most common:

• listing all the multiples method
• prime factorization method

The Listing all the Multiples Method is much easier and more straightforward than the prime factorization method.

Although it is hard to use, the Prime Factorization Method works well for larger numbers which would take a long time to work out using the other method.

We have a dedicated support page all about how to find the LCM using the two methods described above.

There are lots of worked examples to help you understand this concept.

We have split our Least Common Factor worksheets into two main sections: the A group and the B group.

The A group uses the listing all the multiples of both numbers to find the least common multiple.

The A worksheets use the easiest and most straightforward method to find the LCM.

The B group uses the prime factorization method to find the least common multiple.

The B group sheets involve a trickier method which is more appropriate for larger numbers.

The A and B sheets are supported sheets and provide a framework for finding the gcf.

In the third section, there are also harder sheets for more advanced students which can be used with either method.

This section is for students who do not need any extra support or prompts to find the LCM.

The sheets get gradually harder. The last sheet involves finding the LCM of three numbers.

The Least Common Multiple and Greatest Common Factor are often taught alongside each other.

These sheets involve finding both the LCM and GCF on the same sheet.

The first two sheets are easier and keep the numbers for the LCM and GCF separate.

The third and fourth sheets involve finding the LCM and GCF of the same numbers.

The fourth sheet involves 3 numbers rather than 2.

Looking for something a little different to get children to apply their knowledge of GCF and LCM?

Using riddles is a great way to explore and apply your LCM and GCF knowledge by solving problems.

The aim is to find the correct answer out of 6 choices from following the clues.

There are 2 riddles on each sheet.

We have worksheets to help you understand more about factors and multiples.

They are aimed at a 4th/5th grade level.

To find out more about prime factorization, including how it works and to look at some worked examples, take a look at our prime factorization support page.

We have a range of greatest common factor worksheets with numbers up to 100.

Some of our sheets using the listing common factors method.

Some of our sheets use the prime factorization method.

We also have some trickier sheets where you can select the method you want.

Our Greatest Common Factor calculator will tell you the highest common factor between 2 or more numbers.

It will also list the factors of each of the numbers and tell you whether they are coprime or not.

We have worksheets to help you understand more about factors and multiples.

They are aimed at a 4th/5th grade level.

Here you will find a range of more complex Fraction Worksheets for 5th and 6th graders.

At 5th Grade level, children are introduced to adding and subtracting fractions with different denominators. They know and can use equivalent fractions, and can multiply a fraction by whole numbers, as well as adding mixed numbers.

Using these sheets will help your child to:

• add and subtract fractions and mixed numbers;
• understand how to multiply fractions by a whole number;
• understand how to multiply two fractions together, including mixed fractions;
• understand the relationship between fractions and division;
• know how to divide fractions and mixed fractions;
• convert decimals to fractions.

Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.

It will also show you the working out using a choice of two different methods.

There are also some worked examples on the page with explanation of how it works.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.