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202 LearnersLast updated on November 29th, 2024
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.
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
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
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.
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.
Fun Fact
: She loves to read number jokes and games.
