LCM of 6 and 14
2026-02-28 10:32 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-6-and-14

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Last updated on August 5, 2025

LCM is a common multiple, the smallest value between the numbers 6 and 14. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.

What is the LCM of 6 and 14?

LCM of 6 and 14 Using Listing the Multiples

Step 1: Write down the multiples of the numbers. Don’t stop too early.


Multiples of 6 = 6,12,18,24,30,36,42,…


Multiples of 14= 14,28,42,56,…


 Step 2: Find the smallest number common between the written multiples of 6 and 14


The smallest common multiple is 42.


Thus, LCM(6,14) = 42

LCM of 6 and 14 Using Prime Factorization

Step 1: factorize the numbers into its prime factors 


6= 2×3


14  = 7×2


Step 2: find the highest powers of the factors of 6 and 14

Step 3: Multiply the highest powers 


LCM(6,14) = 42

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LCM of 6 and 14 Using Division Method

  • Write the numbers 6,14 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(6,14) = 42
     

Common Mistakes and how to avoid them while finding the LCM of 6 and 14

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 14, make a note while practicing.
 

Problem 1

If you have 1/6 and 1/14 of a cake, what fraction of the cake do you have when combined, and how does it relate to the LCM?

Okay, lets begin

Find a common denominator using LCM:


LCM of 6 and 14 = 42.


Convert fractions:


1/6=7/42 and 1/14=3/42


Combined:


7/42+3/42=10/42=5/21
 

Explanation

This shows the fraction of the cake you have and relates to LCM as it’s based on the common denominator derived from the LCM.
 

Well explained 👍

Problem 2

Machine X stops for maintenance every 14 hours, while machine Y stops every 6 hours. In how long will the machines stop again?

Okay, lets begin

LCM(6,14) = 42
 

Explanation

The machines will stop together in 42 hours. 42 is the LCM of the digits 6 and 14, which in the given case expresses the smallest time interval between the numbers.

Well explained 👍

Problem 3

Compare the LCM of 6 and 14 to the LCM of 4 and 10. Which one is larger?

Okay, lets begin

LCM of 6 and 14 = 42 (calculated earlier).


LCM of 4 and 10:


Prime factorization:


4=22


10=21×51


LCM=22×51=20
 

Explanation

42>20. So, the LCM of 6 and 14 is larger.
 

Well explained 👍

FAQ’s on LCM of 6 and 14

1.List the multiples of 6 and 14.

Multiples of 6 = 6,12,18,24,30,36,42,48,60…


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

2.What is the HCF of 6 and 14?

HCF of 6 and 14 can be found by listing the factors of the numbers → finding the largest common factor from the list of numbers. 


Factors of 6 = 1,2,3,6 


Factors of 14 = 1,2,7,14


HCF (6,14) = 2
 

3.What is the LCM of 6,14 and 16?

LCM (6,14,16) = 336 


336 is the smallest number that appears commonly on the lists of the numbers 6,14 and 16. 
 

4.What is the LCM of 5 and 14?

60 is the smallest number that appears commonly on the lists of the numbers 5 and 14. 


LCM (5,14) = 60 
 

5.What is the LCM of 6,14 and 18?

LCM (6,14,18) = 126 


126 is the smallest number that appears commonly on the lists of the numbers 6,14 and 18. 
 

Important glossaries for LCM of 6 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.