LCM of 2 and 7
2026-02-28 10:18 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 7. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or coordinating any orders.

What is the LCM of 2 and 7?

How to find the LCM of 2 and 7 ?

LCM of 2 and 7 using the Listing Multiples method

The LCM of 2 and 7 can be found using the following steps;


Step 1: Write down the multiples of each number:  


Multiples of 2 = 2,4,6,8,10,12,14,…


Multiples of 7 = 7,12,21,14…

Step 2: Ascertain the smallest multiple from the listed multiples of 2 and 7. 


The LCM (The Least common multiple) 2 and 7 is 14, i.e.,14 is divisible by 2 and 7 leaving no reminders. 

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LCM of 2 and 7 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.


Step 1: Find the prime factors of the numbers:


Prime factorization of 2 = 2


Prime factorization of 7  = 7


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


2,7


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


LCM (2,12) = 2×7 = 14
 

LCM of 2 and 7 using the Division method

The Division Method involves simultaneously 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 has not been divisible previously.

Step 2: The LCM of the numbers is the product of the prime numbers in the first column, i.e, 


2×7= 14


LCM (2,7) = 14

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

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 7, make a note while practicing.
 

Problem 1

What is the least common denominator of 3/2 and 5/7 ?

Okay, lets begin

LCM of 2 and 7 = 14 

Explanation

LCM of a and b is 14. If a is 2, can b be a divisor of 14?
 

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Problem 2

LCM of a and b is 14. If a is 2, can b be a divisor of 14?

Okay, lets begin

 Yes. 
 

Explanation

b can be a divisor of 14. The LCM is the smallest multiple between the numbers, if a  is 2, and the LCM is 14, the other number b must contribute necessary factors to form 14. The divisors of 14 include 7 and 14 itself. 


From the above, we can assume that the other number b can be 14 or 7. 


If 7, is b; → LCM(2,7) = 14, since 2 and 7 have no common factors, the LCM is simply their product. 


If 14, is b → LCM(2,14) = 14, since 14 is a multiple of both 2 and 7.
 

Well explained 👍

Problem 3

Alex and Ben want to share a pizza, but they can’t decide how many slices to cut into. Alex says 2, and Ben says 7. What is the minimum number of slices they can cut the pizza into so that both can have their desired number of slices without leftovers?

Okay, lets begin

The LCM of 2 and 7 is 14.
 

Explanation

 Alex and Ben should cut the pizza into 14 slices, which is the LCM of 2 and 7. 
 

Well explained 👍

FAQs on LCM of 2 and 7

1.What are the multiples of 2 and 7?

Multiples of 2: 2,4,6,8,10,12,14,16,18,20,…

Multiples of 7: 7,14,21,28,35,42,49,56,63,70,… 

The common multiples of 2 and 7 till the 10 multiple is 14. 

2.What is the LCM of 2,7 and 12?

List the prime factors of the numbers; 


Prime factorization of 2 =2 


Prime factorization of 7 = 7 


Prime factorization of 12= 2×2×3

 
Multiply the highest powers ascertained;


LCM (2,7,12) = 2×7×2×3 = 84
 

3.What is the HCF of 2 and 7?

Factors of 2 = 1,2 


Factors of 7 =1,7 


There are no common factors between 2 and 7, the HCF is 1. 
 

4.What is the LCM of 2,5 and 7 ?

List the prime factors of the numbers; 


Prime factorization of 2 =2 


Prime factorization of 7 = 7 


Prime factorization of 5 =5 


Multiply the highest powers ascertained;


LCM (2,5,7) = 2×7×5 =70

5.Are 2 and 7 prime numbers?

Yes, 2 and 7 are prime numbers. They have no factors but themselves and 1. 
 

Important glossaries for LCM of 2 and 7

  • 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.