LCM of 8 and 9
2026-02-28 14:00 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-8-and-9

633 Learners

Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 and 9. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 8 and 9?

How to find the LCM of 8 and 9?

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

LCM of 8 and 9 using the Listing multiples method

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

Steps:

              1. Write down the multiples of each number: 

Multiples of 8 = 8,16,24,32,40,48,56,64,72…

Multiples of 9= 9,18,27,36,45,54,63,72…

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

The LCM of 8 and 9 = 72

Explore Our Programs

LCM of 8 and 9 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.

Steps: 

  1. Find the prime factors of the numbers:

Prime factorization of 8 = 2×2×2

Prime factorization of 9 = 3×3

  1. Multiply the highest power of each factor ascertained to get the LCM: 

LCM (8,9) = 2×2×2×3×3 = 72

LCM of 8 and 9 using the Division Method

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

Steps:

  1. Write down the numbers in a row;
  1. 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.

     

  1. The LCM of the numbers is the product of the prime numbers in the first column, i.e, 

2×2×2×3×3 = 72

LCM (8,9)=72

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

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

Problem 1

1. Bells at a High School ring for the assembly, 8 and 9 minutes apart, respectively. If they ring together at 1:00 PM, when will they ring together again?

Okay, lets begin

The LCM of 8 and 9 is 72.

Explanation

The bells will ring together at 2:12 PM next. The LCM of the given digits is the smallest common multiple using which we ascertain the time asked.

Well explained 👍

Problem 2

A running track is 8 meters long and 9 meters wide. What is the shortest length of a fence needed to enclose the track?

Okay, lets begin

The LCM of 8 and 9 is 72.

Explanation

The smallest length that can be divided by both 8 and 9 can be divided by is 72. The shortest length of the fence is 72 meters.

Well explained 👍

Problem 3

One cookie jar is filled every 8 hours, and the candy jar is filled every 9 hours. If the jars started filling at the same time, how long will it take for the both of them to be filled?

Okay, lets begin

The LCM of 8 and 9 is 72.

Explanation

Therefore, both jars will be filled at the same time again in 72 hours. The LCM (72) of the given digits is the smallest common multiple using which we ascertain the time asked.

Well explained 👍

Problem 4

Two vans arrive at a store every 8 and 9 days, respectively, for a delivery. If they both arrive at the station today, when will they arrive together again?

Okay, lets begin

The LCM of 8 and 9 is 72.

Explanation

The vans will arrive at the station together again in 72 days. The LCM of 8 and 9 is 72, is the smallest common multiple using which we ascertain the time asked.

Well explained 👍

FAQ’s on LCM of 8 and 9

1.Why is the LCM of 8 and 9 not simply their product (8 × 9 = 72) ?

Multiplying gives you the product of the numbers, in this case,72. LCM, however, is the smallest common multiple that can be ascertained following the methods mentioned above.

2.. What is the LCM of 8,9,10?

Follow the below steps: 

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

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

LCM (8,9) = 2×2×2×3×3×5 = 360

3.What is the relationship between the Highest common factor (HCF) and LCM of 8 and 9?

  • The relationship between HCF and LCM is expressed by the formula:  

     LCM(a,b)×HCF(a,b)=a×b

Verifying this, 

LCM(8,9)×HCF(8,9)= 72×1

—> 72=72

This formula shows how the HCF and LCM complement each other.

4.What is the HCF of 8 and 9?

HCF of 8 and 9 can be found by following the below steps; 

  1. List down the prime factors of the numbers
  • Prime factors of 8 =  2×2×2
  • Prime factors of 9 = 3×3
  1. Find the common prime factors —> None 
  2. HCF of 8,9 = 1, as there are no common factors, the HCF of the given numbers is 1. 

5.What is the LCM of 8,9,11?

Follow the below steps: 

  • Find the prime factors of the numbers:

Prime factorization of 8 = 2×2×2

Prime factorization of 9 = 3×3

Prime factorization of 11= 11×1

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

LCM (8,9,11) = 2×2×2×3×3×11 = 792

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.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.

Fun Fact

: She loves to read number jokes and games.