LCM of 3, 5 and 10
2026-02-28 10:17 Diff
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Last updated on August 5, 2025

LCM is the smallest number divisible by 3, 5 and 10. LCM helps to solve problems with fractions, and scenarios like managing supplies and restocking. In this article, we will learn how to find LCM of 3, 5 and 10 by using different methods.

What is the LCM of 3, 5 and 10?

How to find the LCM of 3, 5 and 10?

There are various methods to find the LCM. The methods to find the LCM are:

  • Listing method
  • Prime factorization method  
  • Division method 
     

LCM of 3, 5 and 10 using the Listing Method


In the listing method, we write a multiple of the numbers first and then find the smallest common multiple.

Step 1: Identify the multiples of 3, 5 and 10

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….


Multiples of 5:   5, 10, 15, 20, 25, 30, 35, 40, 45, 50….


Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90….

Step 2: Ascertain the smallest multiple from the listed multiples of 3, 5 and 10

The LCM of 3, 5 and 10 is 30
 

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LCM of 3, 5 and 10 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 3, 5 and 10


Prime factorization of 3: 31


Prime factorization of 5: 51


Prime factorization of 10: 21 × 51

Step 2: Multiply the highest power of each factor ascertained to get the LCM 

LCM of 3, 5 and 10 = 21  × 31 × 51  = 30

LCM of 3, 5 and 10 using the Division Method

This method involves simultaneously dividing the numbers by their prime factors until they become 1 and multiplying the divisors to get the LCM. 


Step 1: Write the numbers in a row, like 3, 5, 10.

Step 2: Start dividing the numbers with prime factors by 2 


From the numbers 3, 5 and 10, only 10 is divisible by 2 (10 ÷
2) which gives 5 as the quotient.

Now the numbers in the row will be 3, 5, 5

Step 3: Move on to the next prime number, 3


From the list 3, 5 and 5, only 3 is divisible by 3 (3 ÷ 3) which gives 1 as the quotient.

Now the numbers in the row will look like 1, 5, 5.

Step 4: Move on to the next prime number 5.


 From the list 1, 5 and 5, only 5 is divisible by 5 (5 ÷ 5) which gives 1 as the quotient.

Now the numbers in the row will look like 1, 1, 1.


Step 5: To find the LCM, multiply all the divisors used 


The divisors used are 2, 3 and 5. The product of 2, 3 and 5 is 30 (2×3×5 = 30)

Common Mistakes and how to avoid them while finding the LCM of 3, 5 and 10

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3, 5 and 10 make a note while practicing.
 

Problem 1

Can you tell whether the LCM of 3, 5 and 10 is 30? Also find the GCF of 3, 5 and 10

Okay, lets begin

Yes, the LCM is 30. The GCF of 3, 5 and 10 is 1.
 

Explanation

We can find the LCM of 30 by listing the multiples of 3, 5 and 10, and finding the least common multiple.


Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….


Multiples of 5:   5, 10, 15, 20, 25, 30, 35, 40, 45, 50….


Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90…

The LCM is 30

           To find the GCF, list the factors of 3, 5 and 10, and find the GCF. Factors of 3 are 1 and 3, factors of 5 are 1 and 5,

the factors of 10 are 1, 2 and 5. So the GCF is 1.

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Problem 2

Runner A runs every 3 minutes in a trail and runner B every 5 minutes and runner C runs every 10 minutes, and both of them start together. When will they both meet at the starting point again?

Okay, lets begin

 The LCM of 3, 5 and 10 is 30.
 

Explanation

Runner A and B will meet at the starting point in 30 minutes, the LCM of 3, 5 and 10 is 30, which is the smallest common time interval for the given digits.
 

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Problem 3

What will be the product when the LCM of 3,5 and 10 is multiplied twice?

Okay, lets begin

 The product will be 900
 

Explanation

The LCM is 30. When 30 is multiplied twice, we get 900 as the product (30 × 30 = 900)

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FAQs on LCM of 3, 5 and 10

1.What is the LCM of 3 5 10 15?

The LCM of 3, 5, 10 and 15 is 30. We can find the LCM using the listing method. Find the multiples of 3, 5, 10 and 15. From the multiple list, find the common multiple that is lower in value.

2.What is the LCM of 3, 4 and 10?

The LCM of 3, 4 and 10 is 60. We can find the LCM using the listing method. Find the multiples of 3, 4, and 10. From the multiple list, find the common multiple that is lower in value. 
 

3.Is the LCM of 3 and 5 15?

Yes, the LCM of 3 and 5 is 15. Using the prime factorization, we can find the LCM. The prime factorization of 3 and 5 is 31  and 51. Multiply them to get 15 as the LCM.
 

4.What is the LCM of 3, 5 and 9?

The LCM of 3, 5 and 9 is 45. Make use of the listing method to find the LCM. Find the multiples of 3, 5 and 9. From the list, identify the common multiple having lower value.
 

5. What is the LCM of 12 and 24?

The LCM of 12 and 24 is 24. Make use of the listing method to find the LCM. Find the multiples of 12 and 24. From the list, identify the common multiple having lower value.
 

Important Glossaries for LCM of 3,5 and 10

  • 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. 
  • LCM: The least common multiple is the smallest number divisible by two or more numbers.
     

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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.