325 LearnersLast updated on May 26th, 2025
LCM of 8 and 10
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 and 10. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 8 and 10?
The LCM of 8 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
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How to find the LCM of 8 and 10?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below
LCM of 8 and 10 using the Listing Multiples Method
The LCM of 8 and 10 can be found using the following steps:
Steps:
1. Write down the multiples of each number
Multiples of 8: 8, 16, 24, 32, 40, …
Multiples of 10: 10, 20, 30, 40, …
2. Ascertain the smallest multiple from the listed multiples
The smallest common multiple of 8 and 10 is 40.
LCM of 8 and 10 using the Prime Factorization Method
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of each number:
Prime factorization of 8 = 2×2×2
Prime factorization of 10 = 2×5
2. Take the highest powers of each prime factor:
Highest power of 2: 23
Highest power of 5: 51
3. Multiply the highest powers to find the LCM:
LCM(8, 10) = 40
LCM of 8 and 10 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
1. Write down the numbers
2. Divide by prime factors:
3. Multiply the divisors:
2×2×2×5=40
So, LCM(8, 10) = 40
Common Mistakes and how to avoid them while finding the LCM of 8 and 10
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8 and 10, make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 8 and 10
This can be avoided by always double-checking the multiples of the numbers 8 and 10 and by not stopping too early. To elaborate, listing 8,16 as multiples of 8 and 10,20,30 as multiples of 10 and assuming 16 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 6 and 8
This can be avoided by learning that the LCM deals with multiples of the numbers 8 and 10, while HCF focuses on divisors of, 8 and 10, i.e., the HCF of 8 and 10 is 2, and the LCM is 40.
Mistake 3
Skipping the prime factors of the given numbers
Errors in prime factorization often include incorrectly factoring 8 and 10. To illustrate, factoring 8 as 2×3 instead of 23 . Doing so will yield the wrong LCM.
Mistake 4
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 8 and 10 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 18 that appears on the list of both 8 and 10.
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Problems and Solutions Involving the LCM of 8 and 10
Problem 1
Goods are received by a shipping company every 8 and 10 days. If the shipments have been received today, when will they next arrive at, the same day?
The LCM of 8 and 10 is 40.
Explanation
The goods will be received next in 40 days. 40, the LCM of the numbers 8 and 10 expresses the smallest time interval between the digits.
Problem 2
A maintenance schedule for projectors is set up every 8 weeks and 10 weeks at a school. If both the projectors are serviced today, in how many weeks will they be serviced again on the same day?
The LCM of 8 and 10 is 40.
Explanation
Both projectors will need maintenance again in 40 weeks.40, the LCM of the numbers 8 and 10 expresses the smallest time interval between the digits.
Problem 3
A car mechanic services a red car every 8 days and a blue car every 10 days. If the cars are serviced today, when will they be serviced next together?
The LCM of 8 and 10 is 40.
Explanation
Both cars will be serviced again in 40 days. 40, the LCM of the numbers 8 and 10 expresses the smallest time interval between the digits.
Problem 4
A yellow bulb is replaced every 8 months and a white bulb is replaced every 10 months. If both of them are replaced today, after how many months will they need to be replaced?
The LCM of 8 and 10 is 40.
Explanation
Both bulbs will need replacement together in 40 months.40, the LCM of the numbers 8 and 10 expresses the smallest time interval between the digits.
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FAQs on LCM of 8 and 10
1.What are the properties of the LCM? Explain using the LCM of 8 and 10.
2.What is the LCM formula using the HCF?
3.Can the LCM exceed the product of given digits 8 and 10?
4.How do you derive the LCM of two decimal numbers? Explain using 8.0 and 10.0.
5.How can children in Indonesia use numbers in everyday life to understand LCM of 8 and 10?
6.What are some fun ways kids in Indonesia can practice LCM of 8 and 10 with numbers?
7.What role do numbers and LCM of 8 and 10 play in helping children in Indonesia develop problem-solving skills?
8.How can families in Indonesia create number-rich environments to improve LCM of 8 and 10 skills?
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Important glossaries for LCM of 8 and 10
- 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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