LCM of 4 and 9
2026-02-28 11:33 Diff
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Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by both 4 and 9. LCM can be solved using listing multiples method, prime factorization or division methods. Unknowingly, we use LCM in scheduling alarms for clocks or the movement of gears in cars.

What is the LCM of 4 and 9?

How to Find the LCM of 4 and 9?

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

LCM of 4 and 9 using the Listing Multiples Method

The LCM of 4 and 9 can be calculated using the following steps:


Step 1: Write down the multiples of each number


Multiples of 4 = 4,8,12,16,20,24,28,32,36,…


Multiples of 9 = 9,18,27,36,…


Step 2:Ascertain the smallest multiple from the listed multiples:


The smallest common multiple is 36.


Thus, LCM(4,9) = 36.

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LCM of 4 and 9 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 each number:


Prime factorization of 4 = 2×2


Prime factorization of 9 = 3 × 3


Step 2:Take the highest powers of each prime factor =2×2×3×3


Step 3: Multiply the highest powers to get the LCM:


LCM(4, 9) =2×2×3×3 = 36.
 

LCM of 4 and 9 using the Division Method

This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

Step 2: repeat untill we get 1 as remainder.

Thus, LCM(4, 9) = 36.
 

Common Mistakes and how to avoid them in LCM of 4 and 9

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 4 and 9 make a note while practicing.
 

Problem 1

LCM of a and b is 36. a=4, find b.

Okay, lets begin

LCM(a,b)=a ×b/HCF(a,b)


36 = 4 ×b/1 


b = 9
 

Explanation

By following the above we find what the other number, b is. In the given question, it is 9. 

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Problem 2

The LCM of a and b is 36 and their HCF is 1. Find their product.

Okay, lets begin

We can find the product by using the formula → LCM(a,b) ×HCF(a,b) = a ×b


a ×b = 36 ×1 


= 36
 

Explanation

The product of two numbers in 36, as verified above. 

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Problem 3

In a neighborhood park, the fountain show is turned on every 4 minutes, and the light show every 9 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?

Okay, lets begin

The LCM of 4 and 9 is 36.
 

Explanation

Both the shows will turn on at the same time in 36 minutes. The LCM of 4 and 9 is 36, which is the smallest common time interval for the given digits.
 

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FAQs on LCM of 4 and 9

1.What is the LCM of 4,9 and 10?

List the prime factors of the numbers;


Prime factorization of 4 = 2×2 


Prime factorization of 9 = 3×3  


Prime factorization of 10 = 2×5


Multiply the highest powers of the numbers 


LCM (4,9,10) = 180

2. What is the LCM of 4,9 and 11?

List the prime factors of the numbers;


Prime factorization of 4 = 2×2 


Prime factorization of 9 = 3×3  


Prime factorization of 11 = 11


Multiply the highest powers of the numbers 


LCM (4,9,11) = 396
 

3.Are 4 and 9 co-prime numbers?

4.What is the HCF of 4 and 9?

Factors of 4 = 1,2,4


Factors of 9 = 1,3,9


There are no common factors between 4 and 9. The HCF of the numbers is 1. 

5.What is the LCM of 4,7 and 9?

List the prime factors of the numbers;


Prime factorization of 4 = 2×2 


Prime factorization of 9 = 3×3  


Prime factorization of 7 = 7


Multiply the highest powers of the numbers 


LCM (4,7,9) = 252
 

Important glossaries for the LCM of 4 and 9

  • 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. 
  • Relatively Prime Numbers:     Numbers that have no common factors other than 1.
  • Fraction: A representation of a part of a whole.
     

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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.