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Last updated on October 1st, 2024

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LCM of 3 and 5

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Foundation
Intermediate
Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 5. 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 5?

The LCM of 3 and 5 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 5?

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 5 using the Listing Multiples Method

 The LCM of 3 and 5 can be found using the following steps:


Step 1: Write down the multiples of each number


Multiples of 3 = 3,6,9,12,15 …


Multiples of 5 = 5, 10,15,20 …

 

Step 2:Ascertain the smallest multiple from the listed multiples

 

The smallest common multiple is 15.


Thus, LCM(3, 5) = 15.

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LCM of 3 and 5 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.

 

Step 1:Find the prime factors of the numbers:


Prime factorization of 3 = 3


Prime factorization of 5 = 5


 Take the highest powers of each prime factor:


Highest power of 3 = 3


Highest power of 5 = 5


Multiply the highest powers to get the LCM:

 

LCM(3, 5) = 3 × 5 = 15

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LCM of 3 and 5 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.

 

Step1: Write the numbers:

 

 

Step 2 : Divide by common prime factors and multiply the divisors: 

 

 

3 × 5 = 15


Thus, LCM(3, 5) = 15.