LCM of 20 and 25
2026-02-28 13:45 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 20 and 25. LCM helps to solve problems with fractions and scenarios like setting an alarm or planning to align events.

What is the LCM of 20 and 25?

How to find the LCM of 20 and 25 ?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below; 
 

LCM of 20 and 25 using the Listing multiples method

To ascertain the LCM, list the multiples of the integers until a common multiple is found. 


Step 1: Writedown the multiples of each number: 


Multiples of 20 = 20,40,60,80,100,…


Multiples of 25 = 25,50,75,100,…


Step 2:  Ascertain the smallest multiple from the listed multiples of 20 and 25. 


The LCM (Least common multiple) of 20 and 25 is 100. i.e.,100 is divisible by 20 and 25 with no reminder.
 

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LCM of 20 and 25 using the Prime Factorization

This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.


Step 1: Find the prime factors of the numbers:


Prime factorization of 20 = 2×2×5


Prime factorization of 25 = 5×5

Step 2:Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: 
LCM (20,25) = 100

LCM of 20 and 25 using the Division Method

The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 


Step 1: Write down the numbers in a row;

 Step 2:Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. 

Step 3:Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

        Step 4The LCM of the numbers is the product of the prime numbers in the first column, i.e., 
LCM (20,25) = 100

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

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

Problem 1

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.

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Problem 2

LCM of 20 and x is 100. Find x.

Okay, lets begin

LCM(20,x) = 100


LCM(a,b)=a×b/HCF(a,b)


Let x be; 


LCM(20,x) = 20×x/HCF(20,x) = 100


Let’s analyze x as; 


Prime factorization of 20 = 5×2×2


Prime factorization of 100 = 5×5×2×2


For the LCM to be 100, x should contribute 22 and 52  to the LCM; 


x could be 5, to suffice for 52 in the prime factorization.


Let us now verify the above assumption; 


LCM(20,25) =100
 

Explanation

 After the above verification, we can say that the missing number is 25.
 

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Problem 3

What is the smallest number that is divisible by both 20 and 25?

Okay, lets begin

The LCM of 20 and 25 as obtained earlier is 100.
 

Explanation

The LCM is the smallest number divisible by the given numbers. In the case of 20 and 25, the smallest number that is divisible by them both is 100.
 

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FAQ’s on LCM of 20 and 25

1.What is the LCM of 15,20 and 25?

Prime factorization of 15 = 5×3


Prime factorization of 20 = 2×2×5


Prime factorization of 25 = 5×5


LCM (!5,20,25) = 300 
 

2.Is 25 the LCM of 5 and 20?

Prime factorization of 5 = 5


Prime factorization of 20 = 2×2×5


LCM(5,20) = 20


No, 25 is not the LCM of 5 and 20. 
 

3.What is the LCM of 10 and 25?

Prime factorization of 10 = 2×5


Prime factorization of 25 = 5×5


LCM(10,25) = 50 
 

4.What is the LCM 7 and 25?

Prime factorization of 7 = 7 


Prime factorization of 25 = 5×5


LCM(7,25) = 175
 

5.What is the LCM of 6 and 25?

Prime factorization of 6 = 2×3


Prime factorization of 25 = 5×5


LCM (6,25) = 150
 

Important glossaries for LCM of 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. 
  • 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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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.