BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon195 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

LCM of 10 and 25

Professor Greenline Explaining Math Concepts

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.

LCM of 10 and 25 for US Students
Professor Greenline from BrightChamps

What is the LCM of 10 and 25?

The LCM of 10 and 25 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.

Professor Greenline from BrightChamps

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; 
 

Professor Greenline from BrightChamps

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.
 

Professor Greenline from BrightChamps

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

Professor Greenline from BrightChamps

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

Max Pointing Out Common Math Mistakes

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. 
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Confusing between LCM and HCF of the numbers 10 and 25 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple). LCM is the smallest number divisible by 10 and 25 while, the largest number that divides them both is the HCF. 
A simple trick to remember is that the HCF is going to be a relatively smaller number than the LCM, as it deals with divisors
 

Max from BrightChamps Saying "Hey"

LCM of 10 and 25, Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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. 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

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

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

LCM of 10,25 = 50


40% of 50 → 40/100×50 = 20
  

Explanation

40% of the LCM is 20. 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s 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.
 

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ’s on LCM of 10 and 25

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

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

3.What is the LCM of 10 and 25?

Math FAQ Answers Dropdown Arrow

4.What is the LCM of 9 and 25?

Math FAQ Answers Dropdown Arrow

5.What is the LCM of 10 and 24?

Math FAQ Answers Dropdown Arrow

6.How can children in United States use numbers in everyday life to understand LCM of 10 and 25 ?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in United States can practice LCM of 10 and 25 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and LCM of 10 and 25 play in helping children in United States develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in United States create number-rich environments to improve LCM of 10 and 25 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

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. 
     
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we believe numbers are more than just figures—they unlock a world full of possibilities! Our goal is to help children throughout the United States master key math skills, focusing today on the LCM of 10 and 25 with special attention to understanding the LCM—in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, keeping score during a Little League baseball game, or managing their allowance to save for cool gadgets, knowing numbers builds confidence for everyday life. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA have unique learning styles, we customize our methods to match each child’s needs. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and exciting all across America. Let’s make the LCM an exciting part of every child’s math adventure!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom