LCM of 7 and 14
2026-02-28 09:01 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 7 and 14. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 7 and 14?

How to find the LCM of 7 and 14 ?

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

LCM of 7 and 14 using the Listing multiples method

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


Step1:Writedown the multiples of each number: 

Multiples of 7 = 7,14,…

Multiples of 14 = 14,28,… 

Step2: Ascertain the smallest multiple from the listed multiples of 7 and 14. 


The LCM (Least common multiple) of 7 and 14 is 14. i.e., 14 is divisible by 7 and 14 with no reminder.
 

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LCM of 7 and 14 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.

Step1: Find the prime factors of the numbers:


Prime factorization of 7 = 7


Prime factorization of 14 = 2×7 

Step2:Take the highest power of each prime factor: 7,2

Step3:Multiply the ascertained factors to get the LCM: 


LCM (7,14) = 7×2 = 14 

LCM of 7 and 14 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;

Step2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.

Step3: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.

Step4: The LCM of the numbers is the product of the prime numbers in the first column, i.e., 


7×2= 14 


LCM (7,14) = 14

Common Mistakes and how to avoid them while finding the LCM of 7 and 14

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 and 14, make a note while practising.

Problem 1

The LCM of 7 and x is 14. Find x.

Okay, lets begin

LCM (7,x) = 14 


x = 14 
 

Explanation

 The LCM of 7 and x must be 14. In a case where x is smaller, the LCM would not be 14,therefore x = 14. 
 

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Problem 2

Verify the relationship between the HCF and the LCM of 7 and 14 using LCM(a,b) × HCF(a,b) = a×b

Okay, lets begin

The LCM of 7 and 14;


Prime factorization of 7 = 7


Prime factorization of 14 = 2×7


LCM(7,14) = 14 


HCF of 7 and 14; 


Factors of 7 = 1,7


Factors of 14 = 1,2,7,14


HCF(7,14) = 7


Verify the ascertained LCM and HCF by applying them in the formula;


LCM(a,b)×HCF(a,b) =a×b 


LCM(7,14)×HCF(7,14) =7×14 


14×7 =98  


98 =98 
 

Explanation

Both sides are equal, hence, the relationship between the HCF and LCM of 7 and 14 is verified. 

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Problem 3

Solve 5/7 + 3/14.

Okay, lets begin

To add 5/7 and 3/14, first, find the LCM of their denominators; 


LCM (7,14) = 14 


Now, we equate the denominators; 


5/7 × 2/2 = 10/14 


3/14 stays as it is, the denominator is already 14. 


Add the fractions; 


10/14+3/14 = 13/14 


The sum is 13/14.
 

Explanation

 By equating the denominators of fractions, we can easily perform arithmetic operations on them. 
 

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Problem 4

Trains A and B arrive every 7 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?

Okay, lets begin

 The LCM of 7 and 14 =14. 
 

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 14 minutes. 

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FAQ’s on LCM of 7 and 14

1.What is the LCM of 7,14 and 21?

Prime factorization of 7 = 7


Prime factorization of 14 = 2×7 


Prime factorization of 21 = 3×7 


LCM (7,14 and 21) = 2×7×3 =  42 
 

2.What do 7 and 14 have in common ?

The numbers 7 and 14 share the common factor 7.

3.List the multiples of 7 and 14.

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


Multiples of 14–14,28,42,56,70,84,98,112,126,140,…
 

4.Is 7 a factor of 56?

Yes, 7 is a factor of 56. To verify the same, we divide the numbers. 56/7 = 8. As there is no remainder left behind, we can say that the number 7 is indeed a factor of 56. 

5.Is 7 a factor of 360?

No, 7 is not a factor of 360. To verify the same, we divide the numbers. 360/7= 51.43. As there is a remainder left behind, we can say that the number 7 is not a factor of 360.
 

Important glossaries for LCM of 7 and 14

  • 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.