LCM of 8, 12 and 18
2026-02-28 23:19 Diff
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Last updated on August 5, 2025

LCM or the least common multiple is the smallest number that is a common multiple of two or more numbers. Scheduling payments for bills and helping musicians maintain rhythm are the uses of LCM. In this topic, we will discuss LCM of 8, 12, and 18.

What is the LCM of 8, 12, and 18

The number that is the least common multiple of 8, 12, and 18 is 72. This number is the smallest number with a positive value divisible by 8, 12, and 18. The LCM of any number will always be positive, as a negative value does not exist based on the concept of LCM. In the case of two irrational numbers, the LCM does not exist. 

How to find the LCM of 8, 12 and 18

There are multiple methods to find the LCM of 8, 12, and 18. The methods are listed below:

  • Listing of Multiples
  • Prime Factorization
  • Division Method
  • Cake Method/ Ladder Method

LCM of 8, 12, and 18 using Listing of Multiples

This method is one of the simplest methods to find the LCM of any given number. In this method, the multiples of each number are listed. The multiples are then compared together to find the common multiple that comes in the list of multiples of all three numbers. The multiples of 8, 12, and 18 are identified and then the common number present in all three lists is the LCM.

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88…

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96…

Multiples of 18 = 18, 36, 54, 72, 90, 108…

72 is the first number that comes out in all three lists of multiples. Hence, 72 is the LCM of 8, 12, and 18.

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LCM of 8, 12, and 18 using Prime Factorization

Here, the prime factorization of the numbers is done to find their LCM. Factorization is done using prime numbers until the number is completely broken down. The common numbers that come in the factorization of all three numbers are taken as a single factor. The multiplication of the prime factors is calculated, and the product obtained will be the LCM.

To find the LCM of 8, 12, and 18, the prime factorization of each number is to be done, and then prime factors are to be multiplied together.

Prime factorization of 8 = 2 x 2 x 2 = 23

Prime factorization of 12 = 2 × 2 × 3 = 22 x 31

Prime factorization of 18 = 2 × 3 × 3 = 21 × 32

The LCM of 8, 12, and 18 = 2 × 2 × 2 × 3 × 3 = 23 × 32 = 72.

LCM of 8, 12, and 18 using the Division Method

The division method involves the division of numbers together in an order. The divisor is to be selected in such a way that the number is able to divide all the numbers and is a prime number. If the number is not divisible,

the number is carried down. Another number is selected by which the division is possible. The division is continued till the remainder is 1 for all the numbers. The divisors with which the division is done are taken together and multiplied to find the LCM of the numbers.

While applying the division method to find the LCM of 8, 12, and 18 with prime numbers till the number becomes completely divided and 1 remains as the remainder. 


Step 1: The numbers 8, 12, and 18 are to be divided together by prime number 2.


Step 2: Division is continued again by 2, and we get 4, 6, and 9.


Step 3: The same step is again repeated by continuing division by 2 we get 2, 3, and 9.


Step 4: Again 2 is taken up for division, and we get 1, 3, and 9.


Step 5: Division is repeated with 3 and the remainders are 1, 1, and 3.


Step 6: 3 is used to continue the division and the remainder are 1, 1, and 1.

The divisors are 2 × 2 × 2 × 3 × 3 = 72, Thus LCM is 72.
 

Common Mistakes and How to Avoid Them in LCM of 8, 12, and 18.

Mistakes are the setbacks that come our way while learning something new. These mistakes can help us learn new things and can give us confidence by forming steps to understand things. The common mistakes given below will help you have a better understanding and will help you avoid them in the future. 

Problem 1

A class has a math lab session every 8 days, a science lab session every 12 days, and a yoga session every 18 days. If all three sessions come together, one day when will be the next day all three classes will come together?

Okay, lets begin

To find the next day the class will have all three sessions together, we need to find the LCM of 8, 12, and 18.

Applying the Prime factorization method:


Prime factors of 8 = 2 x 2 x 2
Prime factors of 12 = 2 x 2 x 3
Prime factors of 18 = 2 x 3 x 3

LCM of 8, 12 and 18 = 2 x 2 x 2 x 3 x 3 = 72.

Explanation

The prime factors of 8, 12, and 18 are to be found, and the prime factorization is to be done to find the LCM of 8, 12, and 18. The answer will be 72 days.

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Problem 2

There are three machines working in a production plant together. The first machine takes 12 hours to produce the final product, the second machine takes 18 hours to produce the final product, and the third machine takes 8 hours to produce the final product. At 9 AM all three machines delivered the final product at the same time, when will all three machines deliver the final product together?

Okay, lets begin

Time taken by each machine to deliver the final product.


Machine 1 = 12 Hours
Machine 2 = 18 Hours
Machine 3 = 8 Hours

Therefore, the prime factors of 8, 12, and 18 are to be found, and the prime factorization is to be done to find the LCM of 12, 18, and 8.

Applying the Prime factorization method:


Prime factorization of 12 = 2 × 2 × 3
Prime factorization of 18 = 2 × 3 × 3
Prime factorization of 8 = 2 × 2 × 2

LCM of 12, 18, and 8 = 2 × 2 × 2 × 3 × 3 = 72.

Therefore, after 9 AM, it will take 72 hours for all three machines to deliver three final products at the same time.

Explanation

The LCM of 12, 18, and 8 are to be found out to find the time after 9 AM when all three machines will deliver the final product together. The LCM is 72 hours.

Well explained 👍

Problem 3

Find the LCM of 8, 12, and 18 by listing the multiples method and divide it by 4.

Okay, lets begin

The multiples of 8, 12, and 18 are 


Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88…

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96…

Multiples of 18 = 18, 36, 54, 72, 90, 108…

From the multiples of 8, 12, and 18, the number that is present in all three lists is to be found out.
The number is 72, thus the LCM of 8,12, and 18 is 72.

Division of LCM of 8, 12, and 18 by 4 = 72 ÷ 4 = 18.


The answer is 18.

Explanation

The LCM of 8, 12, and 18 are to be found, and then the division is to be performed. Here LCM is 72 and by dividing it by 4 the quotient is 18.

Well explained 👍

FAQs on LCM of 8, 12, and 18

1.What is the expanded form of LCM and GCD?

The expanded form of LCM is Least Common Multiple and GCD is Greatest Common Divisor.

2.Is 144 a common multiple for 8, 12 and 18?

Yes, 144 comes in the list of multiples of 8, 12, and 18. Though it cannot be the LCM as it is not the first common number to come in the list of multiples.

3.List the multiples of 18 when it is multiplied by numbers from 1 to 20.

The multiples of 18 when it is multiplied by numbers from 1 to 20 are 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360.

4.What are the methods to find the LCM of two number?

There are various method to find the LCM of two numbers and they are:

  • Listing of Multiples
  • Prime Factorization
  • Division Method

5.How many factors does 12 have, and what are they?

How many factors does 12 have, and what are they?

Important Glossaries for LCM of 8, 12, and 18.

  • Prime Factorization: The process of breaking down the numbers by using the prime factors of that particular number.
  • Multiples: The numbers that are the result of multiplying two numbers with each other.
  • GCD: Greatest Common Divisor or the largest number that is an integer and has the ability to divide two or more numbers.
  • Positive Integers: The whole numbers that more than 0 and extends till infinity. They can be denoted as Z+ in mathematics.
  • Prime numbers: The numbers that can only be divided by two numbers 1 and itself and not by any other numbers.
  • Prime Factors: The factors of a number that are included in the list of prime numbers.

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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.