190 LearnersLast updated on May 26th, 2025
LCM of 6 and 14
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?
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.
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
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
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.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 6 and 14
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.
Mistake 2
Confusing between LCM and HCF of the numbers 6 and 14.
This can be avoided by learning that the LCM deals with multiples of the numbers 6 and 14, while HCF focuses on divisors of, 6 and 14, i.e., the HCF of 6 and 14 is 2, and the LCM is 42.
Mistake 3
Skipping the prime factors of the given numbers.
Errors in prime factorization often include incorrectly factoring 6 and 14. To illustrate, factoring 14 as 72 instead of 7×2. Doing so will yield the wrong LCM.
Mistake 4
Multiplying the numbers directly:
Incorrectly assuming that multiplying the numbers 6 and 14 and assuming the product is the LCM instead of finding the lowest multiple.
Mistake 5
Skipping the LCM in the list method:
Oven, the first common multiples in the list of multiples are ignored due to an oversight, like 42 that appears on the list of both 6 and 14.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
LCM of 6 and 14 Examples
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?
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.
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?
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.
Problem 3
Compare the LCM of 6 and 14 to the LCM of 4 and 10. Which one is larger?
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.
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
FAQ’s on LCM of 6 and 14
1.List the multiples of 6 and 14.
2.What is the HCF of 6 and 14?
3.What is the LCM of 6,14 and 16?
4.What is the LCM of 5 and 14?
5.What is the LCM of 6,14 and 18?
6.How can children in United States use numbers in everyday life to understand LCM of 6 and 14?
7.What are some fun ways kids in United States can practice LCM of 6 and 14 with numbers?
8.What role do numbers and LCM of 6 and 14 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 6 and 14 skills?
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
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.
Explore More numbers
![Important Math Links Icon]()
Previous to LCM of 6 and 14
About BrightChamps in United States
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.
