Easy Way to Explain How to Find the LCM of 8 and 10

Wondering how to explain LCM to a child in the simplest way possible? You’re at the right place. Let’s picture you arranging a party for two groups of friends. However, one of them enjoys cookies given in sets of 8, and the other group would be happy to have everything in sets of 10. You want to ensure that both groups are satisfied with an equal number of items. To find the least common multiple (LCM) of 8 and 10, you need to determine the smallest number that is divisible by both 8 and 10. Let’s explain how to find the lcm of 8 and 10.

What Is the Least Common Multiple, and Why is it Necessary?

You can understand the LCM as the first number on the list of multiples that also takes place on other lists of multiples. In other words, the LCM is the least common multiple of two or more integers. In my example with the party, the least common multiple represents the number of cookies for your guests to make them all happy if some of them prefer to take cookies in sets of 8 and others want everything to come in sets of 10.

How to Calculate the LCM for 8 and 10: Three Fun Ways?

Here are ways for you to explain how to find the lcm of 8 and 10 to your child. Each of them will turn the process into an exciting adventure and help your child understand the concept easier than ever:

Multiples Matching Game as the Funniest Way to Visualize LCM

Start by writing out the lists of multiples of 8 and 10. You have an excellent chance to look at a piece of the list of 8’s multiples I have prepared for you:  

With both written on sticky notes, lay all of them on the table. After which, it becomes a kind of puzzle, turning these pieces of paper and looking for the proper solution. You should look at your lists and recognize the numbers on both of them. These numbers are your common multiples. If you assume their sources from both lists, you generate the subsequent sequence. Moreover, the standard multiple we are looking for is the least one.

Here, the first number that we will see in both lists is 40. So, the LCM of 8 and 10 is 40!

The Counting-up Method

List the multiples of 8 and 10 in separate columns: 8, 16, 24, 32, 40, 48, 56,… and 10, 20, 30, 40, 50, 60, … 

Start at the beginning of the lists and look for the numbers that are the same in the two lists. If they are not the same, list them too and keep going. The first match will be the LCM. As we can see, 40 appears in the 5th place on the list of multiples of 8 and as the 1st on the list of multiples of 10. So, our winner is 40!

The Skipping Challenge

List the Multiples Backward: Start by listing the multiples of the smaller number, which is 8, backward. So, we have 48, 40, 32, 24, 16, 8.

List the Multiples Forward: Then, list the multiples of the larger number, which is 10, in the forward order. So, we have 10, 20, 30, 40, 50, 60.

Comparing the Lists: Now, for each number in the list of multiples of 10, we start checking if it appears in the list of multiples of 8.

Finding the First Common Multiple: We start with 10. Since 10 is not in the list of multiples of 8, we move to the next number, which is 20. 20 is also not in the list of multiples of 8. We continue this process until we find a number that is in both lists.

Identifying the First Common Multiple: When we reach 40, we find that it is both a multiple of 10 and 8. Therefore, 40 is the first common multiple.

The Prime Factorization

Prime Factorization: Begin by breaking down each number into its prime factors. For 8, it’s 2 x 2 x 2, and for 10, it’s 2 x 5.

Identify Unique Prime Factors: Collect all the unique prime factors from both numbers. In this case, we have 2 and 5.

Count the Multiplicity of Each Prime Factor: Now, consider the maximum number of times each prime factor appears in either number. For 2, it appears three times in 8 and once in 10. For 5, it appears once in 10.

Combine the Prime Factors: Combine all the unique prime factors with their respective multiplicities. So, we have 2 x 2 x 2 (three 2s) and 5.

Multiply the Results: Finally, multiply all the combined prime factors together. 2 x 2 x 2 x 5 = 40.

Therefore, using the Prime Factorization method, we find that the least common multiple (LCM) of 8 and 10 is indeed 40.

Bottom Line

Now, you’re a master of LCM and know how to explain it. You just learned four cool ways to find the LCM. You can now explain how to find the LCM of 8 and 10 to your child in whichever way you prefer. If you want to explain more such mathematical concepts to your child in the simplest way possible, consider Mathema.

FAQs

1. Why is the least common multiple (LCM) of two integers important? 

The lowest positive integer divisible by two integers without leaving a remainder is their LCM. It’s helpful in simplifying fractions, adding and subtracting fractions with varying denominators, and solving multivariable equations.

2. Why determine the LCM of 8 and 10 precisely? 

Finding the LCMs of 8 and 10 introduces LCMs and their use in mathematics. Additionally, it develops problem-solving abilities and prepares kids for increasingly complicated mathematical issues.

3. Is there a faster way to determine 8 and 10’s LCM? 

There is no shortcut for computing the LCM of 8 and 10. However, prime factorization may be faster or easier. However, listing multiples and finding the least frequent multiple works well in most cases.

4. Can more numbers be found using the LCM of 8 and 10? 

Absolutely! Finding the LCM of 8 and 10 applies to any pair of numbers. The same techniques apply to determining the LCM by listing each number’s multiples and finding their common multiples. This approach for determining the LCM of any two integers is flexible.

5. What happens when one number is a multiple of another? 

A multiple LCM is the greater of the two numbers. The LCM of 8 and 16 is 16, as 16 is a multiple of 8. It’s unnecessary to search for common multiples when one integer is a multiple of the other.