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Last updated on September 26th, 2024

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LCM of 15,20 and 25

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 15,20 and 25. 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 15,20 and 25?

The LCM of 15,20 and 25 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 15,20 and 25?

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 15,20 and 25 using the Listing Multiples Method

 The LCM of 15,20 and 25 can be found using the following steps:

Step1: Write down the multiples of each number


 Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180…300


 Multiples of 20= 20,40,60,80,100,120,140,160,180,…300


  Multiples of 25 = 25,50,75,100,125,150,175,200…300


 Step2: Ascertain the smallest multiple from the listed multiples


 The smallest common multiple is 300


Thus, LCM (15,20,25) = 300

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LCM of 15,20 and 25 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 15 = 5×3


 Prime factorization of 20 = 5×2×2


Prime factorization of 25 = 5×5

 

 

 

Step2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:


 5×3×2×2×5 = 300


 LCM (15,20,25) = 300
 

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LCM of 15,20 and 25 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.

 

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

 

 

Step 2:  A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.bring down the numbers not divisible by the previously chosen prime number.

 

 

Step 3:Continue dividing the numbers until the last row of the results is ‘1’ .

 

 

 2×2×3×5×5 =  300


Thus, LCM (15,20,25) = 300
 

 

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Important glossaries for the LCM of 15,20 and 25

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.