153 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.
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.
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.
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 India use numbers in everyday life to understand LCM of 6 and 14?
7.What are some fun ways kids in India 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 India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 6 and 14 skills?
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
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