LCM of 15,20 and 25
2026-02-28 11:45 Diff
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Last updated on August 5, 2025

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.

What is the LCM of 15,20 and 25?

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; 

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
 

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
 

Common Mistakes and how to avoid them while finding the LCM of 15,20 and 25

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 15,20 and 25, make a note

while practising.
 

Problem 1

LCM of 15 and x is 60. Find x.

Okay, lets begin

LCM(15,x) = 60


LCM(a,b)=a×b/HCF(a,b)


Let x be; 


LCM(15,x) = 15×x/HCF(15,x) = 60


Let’s analyze x as; 


Prime factorization of 15 = 5×3

Prime factorization of 60 = 5×2×2×3 


For the LCM to be 60, x should contribute 22 to the LCM; 


x could be 20; 22×5 = 20


Let us now verify the above assumption; 


HCF(15,20) = 5


LCM(15,20) = 15×20/5= 60

Explanation

After the above verification, we can say that the missing number is 20.
 

Well explained 👍

Problem 2

LCM (15,20,25) = x. Find the smallest positive integer (n), where n×x is a multiple of 60.

Okay, lets begin

LCM (15,20,25) = x 


We ascertained the LCM of 15,20,25 from the previous calculations.


LCM (15,20,25) = 300 


n is;


n×300 is a multiple of 60


Te same can be rearranged as;


n×300 = k×60, for some integer k 


Divide both the sides 60; 


n×5 = k


n×5 = k implies that n is to be a multiple of 12, 300/60 = 5 and n to be a multiple of 1/5. 


Smallest n = 12
 

Explanation

n is 12, as elaborated above. It satisfies the condition laid the smallest positive integer (n), where n×x is a multiple of 60.

Well explained 👍

Problem 3

a =15, b=20, c=25, use the formula for the LCM of three numbers.

Okay, lets begin

The formula used to find the LCM of 3 digits is; 


LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)


To apply the above formula, calculate the LCM of 15 and 20 first; 

Prime factorization of 15 = 5×3


Prime factorization of 20 = 5×4


LCM (15,20) = 60


Next, find the HCF of 60 (LCM of 15 and 20) and 25; 


Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60 


Factors of 25 = 1,5,25


HCF(60,25) = 5 


We can now substitute the ascertained values into the formula; 


    LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)


    LCM(15,20,25) = LCM(15,20)×25/5


    LCM(15,20,25) = 60×25/5 = 300
 

Explanation

The LCM of numbers 15,20,25 using the formula is 300. The above explained is how we ascertain it. 
 

Well explained 👍

FAQs on LCM of 15,20 and 25

1.List the multiples of 15,20 and 25.

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


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


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

2.What is the LCM of 15,20 and 30?

Prime factorization of 15 = 5×3

Prime factorization of 20 = 5×4


Prime factorization of 30 = 5×2×3 


LCM (15,20, 30) = 5×22×3 = 60

3.What is the LCM of 12,15,20,22 and 25?

Prime factorization of 12 = 2×2×3


Prime factorization of 15 = 5×3


Prime factorization of 20 = 5×2×2


Prime factorization of 22 = 2×11


Prime factorization of 25 = 5×5


LCM (12,15,20,22,25) = 22×3×52×11 = 3300
 

4. What is the LCM of 15,25 and 45?

Prime factorization of 15 = 5×3


Prime factorization of 25 = 5×5


Prime factorization of 45 =  5×3×3


LCM (15,25,45) = 225 
 

5.What is the LCM of 20,25 and 30?

Prime factorization of 20 = 5×2×2


Prime factorization of 25 = 5×5

 Prime factorization of 30 = 5×2×3

 
LCM (20,25,30) = 300
 

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. 
 

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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.

Fun Fact

: She loves to read number jokes and games.