270 LearnersLast updated on May 26th, 2025
LCM of 8 and 14
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 and 14. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 8 and 14?
The LCM of 8 and 14 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
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How to find the LCM of 8 and 14 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 8 and 14 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step 1:Write down the multiples of each number:
Multiples of 8 = 8,16,24,32,40,48,56,…
Multiples of 14 = 14,28,42,56,…
Step 2: Ascertain the smallest multiple from the listed multiples of 8 and 14.
The LCM (Least common multiple) of 8 and 14 is 56. i.e., 56 is divisible by 8 and 14 with no reminder.
LCM of 8 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.
Step 1: Find the prime factors of the numbers:
Prime factorization of 8 = 2×2×2
Prime factorization of 14 = 2×7
Step 2:Take the highest power of each prime factor and multiply the ascertained factors to get the LCM:
LCM (8,14) = 56
LCM of 8 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.
Step 1:Write down the numbers in a row;
Step 2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.
Step 3: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.
Step 4:The LCM of the numbers is the product of the prime numbers in the first column, i.e.,
LCM (8,14) = 56
Common Mistakes and how to avoid them while finding the LCM of 8 and 14
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8 and 14, make a note while practicing.
Mistake 1
Skipping the prime factors of the given numbers.
Errors in prime factorization often include incorrectly factoring 8 and 14. To illustrate, factoring 8 as 2×4 and not factorising it further as 2×2. This leads to inconsistencies while attempting to ascertain the LCM.
Mistake 2
Incorrect use of the formula for LCM
Misapplying the formula LCM(a, b) = a×b/HCF(a, b)
The above formula can be used for two digits only. Substantiated below is how the result will vary.
The HCF of numbers 8 and 14 is 2.
When the formula is used with incorrect HCF—>LCM(a, b) = a×b/HCF(a, b)
LCM (a, b) = 8×14/6 = 18.667
The result varies immensely, the right answer is 56. The same can be verified using the right formula.
LCM (a, b) = 8×14/2 = 56
Mistake 3
Not double-checking the final result
After ascertaining the LCM of the numbers 8 and 14, double-check the result. The correct LCM is divisible by both the numbers, leaving no reminder behind.
To substantiate; 56/8=7
56/14 =4
Since there are no reminders left behind, we can conclude that 56 is the right LCM of the numbers 8 and 14.
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LCM of 8 and 14, Examples
Problem 1
LCM (x,14) = 56. Find x.
LCM (x,14) = x×14/HCF (x,14)
56 = x×14/HCF(x,14)
x= 56×n/14 = 4n
Divisors of 14–1,2,7,14 so n can be only one of them
If n = 1 → 56×1/14 = 4
If n = 2 → 56×2/14 = 8
If n = 7 → 56×7/14 = 28
If n = 14 → 56×14/14 = 56
Explanation
From the above we find that the value of x can be anyone from 4,8,28 or 56.
Problem 2
A common multiple of 8 and 14 is expressed as n. If n is the smallest integer greater than 50, find the value of n.
We know that the LCM(8,14) = 56
To ascertain the smallest multiple of 56 greater than 50, we check the multiples of the number 56,
→ 56,112,168,…
The smallest multiple of 56, greater than 50 is 56.
n = 56
Explanation
The above is how we find the smallest integer greater than a given number.
Problem 3
Trains A and B arrive every 8 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?
The LCM of 8 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 8 and 14
1. What is the HCF of 8 and 14?
2.What is the LCM 8,14 and 16?
3. What is the LCM of 8 and 12?
4.What is the LCM 8,14 and 12?
5.What is the LCM of 9 and 14?
6.How can children in Oman use numbers in everyday life to understand LCM of 8 and 14 ?
7.What are some fun ways kids in Oman can practice LCM of 8 and 14 with numbers?
8.What role do numbers and LCM of 8 and 14 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve LCM of 8 and 14 skills?
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Important glossaries for LCM of 8 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.
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