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Last updated on November 29th, 2024

LCM of 8 and 10

Q: What are the properties of the LCM? Explain using the LCM of 8 and 10.

The LCM is always positive. Divisible by both the given numbers; LCM of 8 and 10 is divisible by both the digits and satisfies; LCM(a, b) × HCF (a, b) = a×b

Q: What is the LCM formula using the HCF?

The LCM can be found using the formula, and as explained with the example given below. LCM (a, b)= a×b/HCF(a, b) For 8 and 10, HCF(8,10)= 2 So, LCM(8,10)=8×10/2 = 4

Q: Can the LCM exceed the product of given digits 8 and 10?

No, the product of the digits 8 and 10 is 80, and the LCM cannot exceed the product. The LCM is often smaller than the product when/if there is a common factor, which there is in the case of 8 and 10.

Q: How do you derive the LCM of two decimal numbers? Explain using 8.0 and 10.0.

To derive the LCM of two decimal numbers, follow the below steps; First, convert the given decimals to whole numbers. In the given case, 8.0 and 10.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (8,10)= 40.

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Foundation

Intermediate

Advance Topics

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

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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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

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.