LCM of 2 and 6
2026-02-28 17:35 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 2 and 6. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 2 and 6?

How to find the LCM of 2 and 6 ?

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

LCM of 2 and 6 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 2 = 2,4,6,8,10,12…


Multiples of 6 = 6,12,18… 


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


The LCM (The Least common multiple) of 2 and 6 is 6. i.e.,6 is divisible by 2 and 6 with no reminder.

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LCM of 2 and 6 using the Prime Factorization

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


Step 1: Find the prime factors of the numbers:


Prime factorization of 2 = 2


Prime factorization of 6 = 2×3  

Step 2: Take the highest power of each prime factor:


2,3


Step 3: Multiply the ascertained factors to get the LCM: 


LCM (2,6) = 2×3 = 6

LCM of 2 and 6 using the Division Method

The Division Method involves 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: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given 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.,

 2×3= 6

LCM (2,6) = 6

Common Mistakes and how to avoid them in LCM of 2 and 6

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 6 make a note while practicing.
 

Problem 1

Use LCM(a,b)=|a×b|/HCF(a,b) to find the LCM of 2 and 6.

Okay, lets begin

Let us assume, a= 2 and b= 6.


Applying the formula; 


LCM(a,b)=|a×b|/HCF(a,b)


HCF of 2,6: 


Factors of 2 = 1,2


Factors of 6 = 1,2,3,6


HCF (2,6) = 2 


LCM(2,6)=|2×6|/2


12/2 = 6
 

Explanation

The above is how we ascertain the LCM of the numbers using the formula

Well explained 👍

Problem 2

Add the fractions 1/2 and 1/6.

Okay, lets begin

First, we find the LCM of the denominators; 


Prime factorization of 2 = 2


Prime factorization of 6 = 2×3  


LCM (2,6) = 6 


Now, we equate the denominators;


1/2 ×3/3 = 3/6 


The denominator of 1/6 is already the LCM, so we do not equate its denominator. 


We proceed to add the fractions; 


3/6 + 1/6 = 4/6 → can be simplified to 2/3.
 

Explanation

The above is how we use LCM to find the sum of fractions. The same process can be applied to other arithmetic operations. 
 

Well explained 👍

Problem 3

LCM of a and b is 6 and the HCF of the same two numbers is 1. Find a and b.

Okay, lets begin

Given; 


LCM (a, b) = 6 


HCF (a, b) = 1


a = 2, b =3

Explanation

For the LCM to be 6 and the HCF to be 1, the numbers have to be coprime, i.e., they have no common factors but 1. 


LCM (3,2) = 6, HCF(2,3) =1 
 

Well explained 👍

FAQ’s on the LCM of 2 and 6

1.Is multiplying 2 and 6 the correct way to find the LCM?

No, multiplying gives you the product of the numbers, in this case,12. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method. 

2.Why is the LCM of 2 and 6, not 6?

6 is not a multiple of 2, so it can’t be the LCM. LCM has to be the smallest number that both 2 and 6 divide into, which is 12. 

3.What is the LCM formula using the HCF?

The method below elaborates on how to derive the LCM using HCF (Highest common factor). An example is also attached to check the validity.  


LCM (a, b)= a×b/HCF(a, b)


For the given numbers 2 and 6, HCF(2,6)=2 


So, LCM(2,6)=2×6/2 = 6


By following the above, we can state that the LCM of numbers 2 and 6 can be found using their HCF, which is 2. 
 

4.Is the LCM of 2 and 6 always a multiple of their HCF?

The LCM is always a multiple of HCF. For the numbers 8 and 20, the HCF is 2, and 6 (the LCM) is a multiple of 2.
 

5.What is the LCM of 2,4,6 and 8 ?

Step 1: Write the numbers

Step 2: Divide by common prime factors

Step 3: Multiply the divisors: So, LCM(2,4,6,8) = 48
 

Important Glossaries for LCM of 2 and 6

  • 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.