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Last updated on November 29th, 2024

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LCM of 8 and 10

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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.

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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

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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.

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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

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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

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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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