BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon282 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

LCM of 3 and 5

Professor Greenline Explaining Math Concepts

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 5. 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.

LCM of 3 and 5 for Australian Students
Professor Greenline from BrightChamps

What is the LCM of 3 and 5?

The LCM of 3 and 5 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. 
 

Professor Greenline from BrightChamps

How to find the LCM of 3 and 5?

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 3 and 5 using the Listing Multiples Method

 The LCM of 3 and 5 can be found using the following steps:


Step 1: Write down the multiples of each number


Multiples of 3 = 3,6,9,12,15 …


Multiples of 5 = 5, 10,15,20 …

 

Step 2:Ascertain the smallest multiple from the listed multiples

 

The smallest common multiple is 15.


Thus, LCM(3, 5) = 15.

Professor Greenline from BrightChamps

LCM of 3 and 5 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 3 = 3


Prime factorization of 5 = 5


 Take the highest powers of each prime factor:


Highest power of 3 = 3


Highest power of 5 = 5


Multiply the highest powers to get the LCM:

 

LCM(3, 5) = 3 × 5 = 15

Professor Greenline from BrightChamps

LCM of 3 and 5 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.

 

Step1: Write the numbers:

 

 

Step 2 : Divide by common prime factors and multiply the divisors: 

 

 

3 × 5 = 15


Thus, LCM(3, 5) = 15.

 

Max Pointing Out Common Math Mistakes

Common Mistakes and how to avoid them while finding the LCM of 3 and 5

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 5, make a note while practicing.
 

 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

 Assuming LCM is always larger than both the numbers
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

 In case of smaller numbers, it is commonly mistaken that their LCM is going to be larger than the both numbers, which is not always the case. To substantiate, the LCM of numbers 2 and 6 is 6, which is equal to the second number of the set and not larger as assumed. In the given case of 3 and 15, however, the LCM is larger than both numbers,15.

Max from BrightChamps Saying "Hey"

LCM of 3 and 5, Examples

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

Problem 1

A number n is divisible by 3 and 5. The value of n is between 20 and 40, find n.

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

To solve for n, we first find the LCM of the numbers 3 and 5; 


Prime factorization of 3 = 31


Prime factorization of 5 = 51


LCM (3,5) = 15 


15×2 = 30, a multiple of both 3 and 5. 
 

Explanation

We find a multiple of 15, that falls in the range of 20 and 40 is; 15 ×2 = 30, which is divisible by both 3 and 5. 

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

Problem 2

Verify a×b = LCM (a,b) ×HCF(a,b) for 3 and 5.

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

a = 3, b= 5 

 

a×b = LCM (a,b) ×HCF(a,b)


3×5 = LCM (3,5) ×HCF(3,5)


15 = 15 ×1


15 = 15

Explanation

LHS = RHS in the above solution, the relationship is hence verified.

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

Problem 3

The product of a and b is 45, and the HCF is 1. a = 3, find the LCM.

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

We know that;  a×b = LCM (a,b) ×HCF(a,b)


Given; 3×b = 45, HCF(3,b)= 1


Applying the same in the formula; 


45 = LCM (3,b) ×1


LCM (3,b) = 45/1 = 45

 

Now we solve for b - 3×b = 45


b = 45/3 = 15 
 

Explanation

The other number is 15, LCM(3,15) = 15. 
 

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

Problem 4

A car mechanic services a red car every 3 days and a blue car every 5 days. If the cars are serviced today, when will they be serviced next together?

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

 The LCM of 3 and 5 is 15. 

Explanation

 Both cars will be serviced again in 15 days, which is the smallest time interval between the digits. 
 

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

FAQs on the LCM 3 and 5

1.What are the first two LCMs of the numbers 3 and 5 ?

Math FAQ Answers Dropdown Arrow

2.What is the Least common denominator (LCD) of 3 and 5 ?

Math FAQ Answers Dropdown Arrow

3.What do 3 and 5 have in common ?

Math FAQ Answers Dropdown Arrow

4.What is the LCM of 3,5 and 7?

Math FAQ Answers Dropdown Arrow

5.How to find multiples of 3 and 5 ?

Math FAQ Answers Dropdown Arrow

6.How can children in Australia use numbers in everyday life to understand LCM of 3 and 5?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in Australia can practice LCM of 3 and 5 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and LCM of 3 and 5 play in helping children in Australia develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in Australia create number-rich environments to improve LCM of 3 and 5 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

About BrightChamps in Australia

At BrightChamps, numbers mean more than just figures—they open up a world of possibilities! Our mission is to help children throughout Australia develop key math skills, focusing on the LCM of 3 and 5 with a special focus on understanding the LCM—in an engaging, fun, and easy-to-learn way. Whether your child is figuring out how fast a roller coaster runs at Luna Park Sydney, keeping track of cricket scores, or managing their allowance for the latest gadgets, mastering numbers builds confidence in everyday situations. Our interactive lessons make learning enjoyable and straightforward. Because kids in Australia learn in many different ways, we customize our teaching to suit each child. From Sydney’s vibrant streets to the stunning beaches of the Gold Coast, BrightChamps brings math alive, making the LCM an exciting part of every child’s journey!
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