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Last updated on May 26th, 2025

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LCM of 6 and 14

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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.

LCM of 6 and 14 for UK Students
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What is the LCM of 6 and 14?

The LCM of 6 and 14 is 42. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below. 
 

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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

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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
     
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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.
 

Mistake 1

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Listing incorrect/overlooking multiples for the given numbers 6 and 14 
 

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This can be avoided by always double-checking the multiples of the numbers 6 and 14 and by not stopping too early. To elaborate, listing 6,12 as multiples of 6 and 14,28 as multiples of 14 and assuming 12 is the LCM. 

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LCM of 6 and 14 Examples

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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?

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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.
 

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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?

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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.

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Problem 3

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

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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.
 

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FAQ’s on LCM of 6 and 14

1.List the multiples of 6 and 14.

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2.What is the HCF of 6 and 14?

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

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4.What is the LCM of 5 and 14?

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

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6.How can children in United Kingdom use numbers in everyday life to understand LCM of 6 and 14?

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7.What are some fun ways kids in United Kingdom can practice LCM of 6 and 14 with numbers?

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8.What role do numbers and LCM of 6 and 14 play in helping children in United Kingdom develop problem-solving skills?

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9.How can families in United Kingdom create number-rich environments to improve LCM of 6 and 14 skills?

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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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About BrightChamps in United Kingdom

At BrightChamps, we know numbers are far more than mere digits—they open doors to endless opportunities! We aim to support children all over the United Kingdom in mastering essential math skills, with today’s spotlight on the LCM of 6 and 14 and a special focus on understanding the LCM—in a lively, enjoyable, and easy-to-understand way. Whether your child is working out how fast a roller coaster travels at Alton Towers, tracking scores at a local football match, or budgeting pocket money for the latest gadgets, mastering numbers helps build their everyday confidence. Our interactive lessons make learning fun and straightforward. Since children in the UK learn in diverse ways, we adapt our teaching to suit each individual. From the bustling streets of London to the scenic coastlines of Cornwall, BrightChamps makes math relatable and exciting throughout the UK. Let’s bring the LCM to life for every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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