LCM of 10 and 25
2026-02-28 23:23 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 10 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 10 and 25?

How to find the LCM of 10 and 25 ?

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

LCM of 10 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 :Write down the multiples of each number: 


Multiples of 10 = 10,20,30,40,50,…


Multiples of 25 = 25,50,75,…


Step 2: Ascertain the smallest multiple from the listed multiples of 10 and 25. 


The LCM (Least common multiple) of 10 and 25 is 50. i.e., 50 is divisible by 10 and 25 with no reminder.
 

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LCM of 10 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 10 = 2×5


Prime factorization of 25 = 5×5

 Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: 


LCM (10,25) = 50

LCM of 10 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 3: The LCM of the numbers is the product of the prime numbers in the first column, i.e., 
LCM (10,25) = 50

Common Mistakes and how to avoid them in LCM of 10 and 25

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 25, make a note while practicing. 
 

Problem 1

The LCM of a and b is 50. Given a is 10, find b.

Okay, lets begin

Using the formula; 


LCM(a,b) =a×b/HCF(a,b)  


a =10, b= ?


LCM (a, b) = 50


The factors of 10 (a) are — 1,2,5,10; so we can assume that the HCF is one of these numbers.

 
By testing the values, we find the possible values of b. 


Testing for 10; 


25 = 10×b/10 


b = 25


Testing for 5; 


25 = 10×b/5 


b = 12.5 


Testing for 2; 


25 = 10×b/2 


b = 5


Testing for 1; 


25 =10×b/1 


b = 2.5 → cannot be true, 2.5 is not a whole number

Explanation

b is possibly one of 5 and 25. 
 

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Problem 2

If a number is 40% of the LCM of 10 and 25, find the number.

Okay, lets begin

LCM of 10,25 = 50


40% of 50 → 40/100×50 = 20
  

Explanation

40% of the LCM is 20. 
 

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Problem 3

Trains A and B arrive every 10 minutes and 25 minutes at the station at the same time. In how long will they arrive together again?

Okay, lets begin

The LCM of 10 and 25 = 50
 

Explanation

The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 25 minutes.
 

Well explained 👍

FAQ’s on LCM of 10 and 25

1.What is the relationship between the HCF and LCM of 10 and 25?

HCF(a,b)×LCM(a,b)=a×b


HCF of 10,25 → 5 


LCM of 10,25 → 50 


5×50=10×25


250 = 250
 

2.What is the LCM of 10,25,35 and 40?

Prime factorization of 10 = 2×5


Prime factorization of 25= 5×5


Prime factorization of 35  = 5×7


Prime factorization of 40  = 5×2×2×2


LCM (10,25,35,40) = 1400
 

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 of 9 and 25?

Prime factorization of 9 = 3×3


Prime factorization of 25= 5×5


LCM(9,25) = 225
 

5.What is the LCM of 10 and 24?

Prime factorization of 10 = 2×5


Prime factorization of 24 = 2×2×2×3


LCM (10,24) = 60
 

Important glossaries for LCM of 10 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.