BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon169 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

LCM of 8,9 and 10

Professor Greenline Explaining Math Concepts

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8,9 and 10. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or grouping any items.

LCM of 8,9 and 10 for Bahraini Students
Professor Greenline from BrightChamps

What is the LCM of 8,9 and 10?

The LCM of 8,9 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators. 

Professor Greenline from BrightChamps

How to find the LCM of 8,9 and 10?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below; 
 

Professor Greenline from BrightChamps

LCM of 8,9 and 10 using the Listing multiples method

The LCM of 8,9 and 10 can be found using the following steps;


Step 1: Write down the multiples of each number: 


Multiples of 8 = 8,16,24,32,…


Multiples of 9=  9,18,27,36,45,54,63,…


Multiples of 10 = 10,20,30,40,50,60,70,80,90,100,110,…

 

Step 2: Ascertain the smallest multiple from the listed multiples of 8 and 9. 


The LCM of 8,9 and 10 =360

Professor Greenline from BrightChamps

LCM of 8,9 and 10 using the Prime Factorization

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.


Step 1:  Find the prime factors of the numbers:


Prime factorization of 8 = 2×2×2


Prime factorization of 9 = 3×3


Prime factorization of 10 = 2×5


Step 2: Multiply the highest power of each factor ascertained to get the LCM: 


LCM (8,9) = 2×2×2×3×3×5 = 360

Professor Greenline from BrightChamps

LCM of 8,9 and 10 using the Division Method

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

 

 Step 1: Write down the numbers in a row;

 

 

Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

 

 

 

Step 3: The LCM of the numbers is the product of the prime numbers in the first column, i.e, 


2×2×2×3×3×5 = 360


LCM (8,9,10)=360

 

Max Pointing Out Common Math Mistakes

Common Mistakes and how to avoid them while finding the LCM of 8,9 and 10

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8,9 and 10 make a note while practicing.
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

 Misinterpreting word problems
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

In problems that deal with scheduling or repeating events one may assume they need to perform addition or subtraction instead of finding the LCM. 
 

Max from BrightChamps Saying "Hey"

LCM of 8,9 and 10 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

The LCM (8,9,x) is 360. Find x.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

To find x, we use the formula → LCM(a,b,c) = LCM(LCM(a,b),c)/HCF(a,b,c)


LCM (8,9)=72 


But we already know that; LCM of 8,9, x = 360


The missing number must be 10: 


LCM(72,10) = 360
 

Explanation

the above is how we ascertain x, the third number. 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

One side of the triangular running track is 8 meters long, the second 9 meters long, and the third 10 meters long. What is the shortest length of a fence needed to enclose the track?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The LCM of 8,9 and 10 = 360
 

Explanation

The smallest length that can be divided by both 8,9 and 10 can be divided by is 360. The shortest length of the fence is 360 meters. 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

a = 8, b=9, c=10, verify in LCM(a,b,c)×HCF(a,b,c) =a×b×c

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

 LCM(a,b,c)×HCF(a,b,c) =a×b×c


HCF (8,9,10) = 1


LCM(8,9,10) = 360


LCM(a,b,c)×HCF(a,b,c) =a×b×c


360×1=8×9×10


360 is not equal to 720. 
 

Explanation

The formula is only valid when all prime factors are accounted for and the values for HCF and LCM are to be consistent.
 

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ’s on LCM of 8 and 9 and 10

1.What is the HCF of 8,9 and 10?

Math FAQ Answers Dropdown Arrow

2.List the common factors of 8,9,10,15.

Math FAQ Answers Dropdown Arrow

3.What is the LCM of 8,10 and 15?

Math FAQ Answers Dropdown Arrow

4.What is the LCM of 8,9 and 11?

Math FAQ Answers Dropdown Arrow

5.What is the LCM of 8,9 and 12?

Math FAQ Answers Dropdown Arrow

6.How can children in Bahrain use numbers in everyday life to understand LCM of 8,9 and 10?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in Bahrain can practice LCM of 8,9 and 10 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and LCM of 8,9 and 10 play in helping children in Bahrain develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in Bahrain create number-rich environments to improve LCM of 8,9 and 10 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important glossaries for the LCM of 8 and 9

  • Multiple: A number and any integer multiplied. 

 

  • Prime Factor: A natural number (other than 1) that has factors that are one and itself.

 

  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 

 

  • Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 

 

  • Relatively Prime Numbers:Numbers that have no common factors other than 1.

 

  • Fraction: A representation of a part of a whole.
Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, numbers are more than just digits—they open doors to countless opportunities! We assist children across Bahrain in mastering vital math skills, focusing today on the LCM of 8,9 and 10 with special focus on understanding the LCM—in a way that’s lively, enjoyable, and easy to understand. Whether your child is working out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, tracking scores at local football matches, or managing their allowance for gadgets, mastering numbers boosts confidence for everyday life. Our interactive lessons make learning both fun and simple. Since kids in Bahrain learn differently, we tailor our approach to fit every learner. From Manama’s lively city to peaceful beaches, BrightChamps brings math to life, making the LCM a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom