LCM of 2,3 and 7
2026-02-28 23:29 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-2-3-and-7

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Last updated on August 5, 2025

The LCM comes in use when we need to find a shared pattern between numbers that seem unrelated. We apply LCM to synchronize cycles or schedules, syncing digital signals and finding compatible frequencies in technology. In this article, we’ll take a look at the LCM of 2,3 and 7.

What is the LCM of 2,3 and 7?

LCM of 2,3 and 7 using the Listing Multiples Method

 The LCM of 2,3 and 7 can be found using the following steps:


Step 1: Write the multiples of each number


Multiples of 2 = 2,4,6,8,10,12,14,…42,…


Multiples of 3  = 3,6,9,12,18,…42


Multiples of 7 = 7,14,21,28,35,42,…


LCM(2,3,7) = 42


Step 2: Find the smallest multiple from the listed multiples


The smallest common multiple is 42.


Thus, LCM (2,3,7) = 42

LCM of 2,3 and 7 using the Prime Factorization Method

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 3 = 31


 Prime factorization of 2 = 21


Prime factorization of 7 = 71


Step 2:Take the highest powers of each prime factor. Multiply the highest powers to get the LCM


LCM(2,3,7) = 42

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LCM of 2,3 and 7 using the Division Method

  • Write the numbers 2,3 and 7 in a row 
  • Divide them by their common prime factors, if there is one
  • Carry forward the numbers that are left undivided by the previously chosen factor
  • Continue dividing until the remainder is ‘1’ 
  • Multiply the divisors to find the LCM
  • LCM (2,3,7) = 42

Common Mistakes and how to avoid them while finding the LCM of 2,3 and 7

It is not unusual that kids make mistakes when trying to find the LCM of the numbers 4,5 and 7. 
This may be due to unclear understanding of the concept or confusion. Make sure to avoid these!
 

Problem 1

LCM (2,6,7) = LCM(2,3,7) → Verify.

Okay, lets begin

LCM of 2,6,7; 


Prime factorization of 2 = 21 


Prime factorization of 6 =  21×31


Prime factorization of 7 = 71


LCM(2,6,7) = 42 


LCM of 2,3,7; 


Prime factorization of 3 = 31


Prime factorization of 2 = 21


Prime factorization of 7 = 71


LCM(2,3,7) = 42
 

Explanation

LHS is equal to the RHS, the statement is true.

Well explained 👍

Problem 2

a=2, b=3, c=7. Verify using → LCM(a,b,c) = LCM(LCM(a,b),c)

Okay, lets begin

LCM of 2,3;


Prime factorization of 3 = 31


Prime factorization of 2 = 21


LCM(2,3) = 6 


Use the obtained LCM in the below; 


LCM of 6,7; 


Prime factorization of 6 =  21×31


Prime factorization of 7 = 71


LCM(6,7) = 42 

Explanation

LCM(2,3,7) =42, it verifies with the given formula. 
 

Well explained 👍

Problem 3

Find x, LCM(3,9,x) = 72

Okay, lets begin

We know that the LCM of 3,9 = 9 
The prime factorization of 72 = 23×32
The LCM of 3,9 already includes 32, and the factor of x must include 23, which is 8.
 

Explanation

By following the above assumption we assume that the value of x is 8. 
 

Well explained 👍

FAQs on LCM of 2,3 and 7

1.What is the LCM of 2,4 and 7?

28 is the smallest number that appears commonly on the list of the numbers 2,4 and 7.
LCM (2,4,7) = 28
 

2. What is the GCF of 3, 9, and 12?

Factors of 3 = 1, 3 


Factors of 9 = 1, 3, 9 


Factors of 12 = 1, 2, 3, 4, 6


The common factor between the numbers 3, 9, and 12 is 3. The GCF (3,9,12) = 3 
 

3.Find the LCM of 3 and 4.

LCM (3,4) = 12. 12 is the smallest number that appears commonly on the lists of the numbers 3 and 4. 
 

4.What is the LCM of 9 and 12?

36 is the smallest number that appears commonly on the lists of the numbers 9 and 12. LCM (9,12) = 36 

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

LCM (4,2,8) = 8. 


8 is the smallest number that appears commonly on the lists of the numbers 2,4 and 8
 

Important glossaries for the LCM of 2,3 and 7

  • Multiple — product of a number and a natural integer 
  • Prime factor — number one gets after prime factorization any given number 
  • Prime factorization — the process of breaking the number into its prime factors. 

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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.