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Last updated on December 2nd, 2024

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LCM of 3, 4, and 5

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 9. 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 3 and 9?

The LCM of 3 and 9 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 3 and 9?

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 3 and 9 using the Listing Multiples Method

The LCM of 3 and 9 can be found using the following steps:

Steps:

Write down the multiples of each number

  â€” Multiples of 3 = 3, 6, 9, 12, 15, 18, …

  â€” Multiples of 9 = 9, 18, 27, 36, …

Ascertain the smallest multiple from the listed multiples

  â€” The least common multiple is 9.

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LCM of 3 and 9 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 the numbers:

  â€” Prime factorization of 3 = 3

  â€” Prime factorization of 9 = 3 × 3

  1. Take the highest powers of each prime factor:

  â€” Highest power of 3 = 3²

— Multiply the highest powers to get the LCM:  

  LCM(3, 9) = 3² = 9.

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LCM of 3 and 9 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.

Steps:

— Write the numbers, divide by common prime factors and multiply the divisors.


 

  â€” 3 × 3 = 9

 

Thus, LCM(3, 9) = 9.

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Important glossaries for LCM of 3 and 9

 

  • 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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