LCM of 3 and 5
2026-02-28 23:31 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 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.

What is the LCM of 3 and 5?

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; 
 

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.

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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

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.

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.
 

Problem 1

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

Okay, lets 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. 

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Problem 2

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

Okay, lets 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.

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Problem 3

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

Okay, lets 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. 
 

Well explained 👍

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?

Okay, lets 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. 
 

Well explained 👍

FAQs on the LCM 3 and 5

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

Write down the multiples of each number

  •  Multiples of 3 = 3,6,9,12,15,18,21,24,27,30 …
  • Multiples of 5 = 5, 10,15,20,25,30 …
  •   Ascertain the smallest multiple from the listed multiple
  • The first smallest common multiple is 15 followed by 30. 

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

Both 3 and 5 are prime numbers and share no common factors, therefore, the LCD is 3x5=15.
 

3.What do 3 and 5 have in common ?

The only common factor of 3 and 5 is 1, the given numbers are prime. 


The common multiples of 3 and 5 are; 15,30,45,…

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

There are no common factors between the numbers, as they are all prime. 
LCM of the numbers = 3×5×7 = 105
 

5.How to find multiples of 3 and 5 ?

A simple way to find the multiples is adding the number to the next digit. 


Begin with 3, and keep adding the same multiple fold, do the same for 5. 


Multiples of 3 = 3,6,9,12,15,18,21,24,27,30 …


Multiples of 5 = 5, 10,15,20,25,30 …
 

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.