LCM of 6 and 18
2026-02-28 23:22 Diff
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Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 18. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycles of events.

What is the LCM of 6 and 18?

How to find the LCM of 6 and 18 ?

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

LCM of 6 and 18 using the Listing multiples method

To ascertain the LCM, list the multiples of the integers until a common multiple is found.


Step 1: Writedown the multiples of each number: 


Multiples of 6 = 6,12,18,…


Multiples of 18 = 18,36,…


Step 2: Ascertain the smallest multiple from the listed multiples of 6 and 18. 


The LCM (Least common multiple) of 6 and 18 is 18. i.e., 18 is divisible by 6 and 18 with no reminder.
 

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LCM of 6 and 18 using the Prime Factorization method

This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.


Steps 1: Find the prime factors of the numbers:


Prime factorization of 6 = 2×3


Prime factorization of 18 = 2×3×3

  
Step 2:Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: 


LCM (6,18) = 18

LCM of 6 and 18 using the Division Method

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

Step1:Write down the numbers in a row;

 Step 2:Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. 

Step 3: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 4:The LCM of the numbers is the product of the prime numbers in the first column.

Common Mistakes and how to avoid them while finding the LCM of 6 and 18

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 18, make a note while practising. 

Problem 1

The LCM of a and b is 36. Given a is 6, find b.

Okay, lets begin

b is possibly one of 12,18 and 36. 
 

Explanation

Using the formula; 


LCM(a,b) =a×b/HCF(a,b)  


a =6, b= ?


LCM (a, b) = 36 


The factors of 6 (a) are — 1,2,3,6; so we can assume that the HCF is one of these numbers. 


By testing the values, we find the possible values of b. 


Testing for 6; 


36 = 6×b/6 


b = 36 


Testing for 3; 


36 = 6×b/3 


b = 18 


Testing for 2; 


36 = 6×b/2 


b = 12 


Testing for 1; 


36 =6×b/1 


b = 6 → cannot be true, as the LCM of 6,6 is 6. 

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Problem 2

If the HCF of 6 and 18 is 6, using the relationship between 6 and 18, find the LCM.

Okay, lets begin

Given values; 


HCF = 6


a = 6 


b = 18


Using the formula; 


LCM (a,b)=a×b/HCF(a, b)


LCM (6,18)= 6×18/6 =18

Explanation

 The relationship between HCF and LCM, as explained above allows us to find the LCM without direct calculation. 
 

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Problem 3

Trains A and B arrive every 6 minutes and 18 minutes at the station at the same time. In how long will they arrive together again?

Okay, lets begin

 The LCM of 6 and 18 =18. 
 

Explanation

The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 18 minutes. 

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FAQ’s on LCM of 6 and 18

1.What is the HCF of 6 and 18?

Factors of 6 = 1,2,3,6 


Factors of 18 = 1,2,3,6,9,18


HCF(6,18) = 6 
 

2.What are the factors of 6 and 18?

Factors of 6 = 1,2,3,6 


Factors of 18 = 1,2,3,6,9,18


Common factors: 1,2,3,6 
 

3.Is 6 a factor of 69?

No, 6 is not a factor of 69. When divided, a remainder is left behind. 

4.What is the LCM of 3,6 and 18?

  • Prime factorization of 3 = 3 
  • Prime factorization of 6 = 2×3
  • Prime factorization of 18 = 3×3×2
  • LCM (3,6,18) = 18

5.Is 6 a factor of 0?

Yes, 6 is a factor of 0. In fact, all non-zero numbers are factors of 0. 
 

Important glossaries for LCM of 6 and 18

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.
 

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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.