LCM of 5 and 9
2026-02-28 01:07 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 5 and 9. 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 5 and 9?

How to Find the LCM of 5 and 9?

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


LCM of 5 and 9 using the Listing Multiples Method


The LCM of 5 and 9 can be found using the following steps:


Step 1: Write down the multiples of each number


Multiples of 5 = 5,10,15,20,25,30,35,40,45,…


Multiples of 9 = 9, 18, 27, 36,45,54, …


Step 2:Ascertain the smallest multiple from the listed multiples


The least common multiple is 45.

LCM of 5 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.

Step1: Find the prime factors of the numbers


Prime factorization of 5 = 5


Prime factorization of 9 = 3 × 3


Step2: Take the highest powers of each prime factor


Highest power of 5 = 5


Highest power of 9 = 32


Step3 : Multiply the highest powers to get the LCM:  


  LCM(5, 9) = 5×32 = 45

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LCM of 5 and 9 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.
 

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

Step 2 : keep dividing till we get 1 as remainder.

5 × 3 × 3 = 45

Thus, LCM(5, 9) = 45
 

Common Mistakes and how to avoid them in LCM of 5 and 9

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 5 and 9, make a note while practicing.
 

Problem 1

LCM of a and b is 45. a=5, find b.

Okay, lets begin

We can find the value of b using → LCM(a,b) = a×b/HCF(a,b)


LCM(a,b)= 45 


45=5×b/1 


Now we solve for b. 


b = 45/5 = 9

Explanation

 By following the above we ascertain the missing digit from the given LCM.

Well explained 👍

Problem 2

LCM(a,b)×HCF(a,b) = a×b, verify the relationship between the HCF and LCM of 5 and 9 using the given formula.

Okay, lets begin

LCM(a,b)×HCF(a,b) = a×b


LCM of 5,9; 


Prime factorization of 5 = 5


Prime factorization of 9 = 3 × 3


LCM (5,9) = 45 


HCF of 5,9; 


Factors of 5 = 1,5 


Factors of 9 = 1,3,9 


HCF(5,9) = 1 


Applying the above in the given formula; 


LCM(a,b)×HCF(a,b) = a×b


45×1 = 9×5


45=45
 

Explanation

LHS=RHS, the relationship stands true in the case of numbers 5 and 9.
 

Well explained 👍

Problem 3

A yellow bulb is replaced every 5 months and a white bulb is replaced every 9 months. If both of them are replaced today, after how many months will they need to be replaced?

Okay, lets begin

The LCM of 5 and 9 is 45.
 

Explanation

Both bulbs will need replacement together in 9 months. The LCM of 5 and 9 is 45 which is the smallest time interval between the digits. 

Well explained 👍

FAQs on LCM of 5 and 9

1.What is the LCD (Lowest common denominator) of 5 and 9?

LCD of 5 and 9 = 45, the smallest number both 5 and 9 divide into.

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

Find the prime factors of the numbers:


Prime factorization of 5 = 5


Prime factorization of 7=7


Prime factorization of 9 = 3 × 3


Take the highest powers of each prime factor:


Highest power of 5 = 5


Highest power of 7 = 7 


Highest power of 9 = 32


Multiply the highest powers to get the LCM:  


LCM(5,7, 9) = 5×7×32 = 315
 

3.What is the LCM of 9,5 and 18?

 Find the prime factors of the numbers:


Prime factorization of 5 = 5


Prime factorization of 18= 3 × 3 × 2


Prime factorization of 9 = 3 × 3


Take the highest powers of each prime factor:


Highest power of 5 = 5


Highest power of 18  = 32, 2 


Highest power of 9 = 32


Multiply the highest powers to get the LCM:  


 LCM(5,18, 9) = 5×2×32 = 90
 

4.What is the LCM of 5,9 and 12 ?

Find the prime factors of the numbers:


Prime factorization of 5 = 5


Prime factorization of 12= 3 × 2 × 2


Prime factorization of 9 = 3 × 3


Take the highest powers of each prime factor:


Highest power of 5 = 5


Highest power of 12  = 22, 3


Highest power of 9 = 32


Multiply the highest powers to get the LCM:  


LCM(5,12, 9) = 5×22×32 = 180 

5.What is the HCF of 5 and 9?

5 and 9 share no common factors, therefore the HCF of the numbers 5 and 9 is 1. 

Important glossaries for LCM of 5 and 9

  • 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. 
  • 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.