LCM of 9 and 15
2026-02-28 12:54 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-9-and-15

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Last updated on August 5, 2025

LCM is a common multiple, the smallest value between the numbers 3 and 8. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.

What is the LCM of 9 and 15?

LCM of 9 and 15 Using Listing the Multiples

Step 1: Write down the multiples of the numbers. Don’t stop too early.


Multiples of 9 = 9,18,27,36,45,54,…


Multiples of 15 = 15,30,45,60,75,…


Step 2: Find the smallest number common between the written multiples of 9 and 15


The smallest common multiple is 45


Thus, LCM(9,15) = 45
 

LCM of 9 and 15 Using Prime Factorization

Step 1: factorize the numbers into its prime factors 


9 = 3×3


15 = 3×5


Step 2:find the highest powers of the factors of 9 and 15


Step 3:Multiply the highest powers 


LCM(9,15) = 45

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LCM of 9 and 15 Using Division Method

  • Write the numbers 9,15 in a row 
  • Divide them by their common prime factors, if there is one
  • Carry forward the numbers that are left undivided by the previously chosen factor
  • Continue dividing until the remainder is ‘1’ 
  • Multiply the divisors to find the LCM
  • LCM(9,15) = 45
     

Common Mistakes and how to avoid them while finding the LCM of 9 and 15

Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 9 and 15. Try to avoid them. 
 

Problem 1

If the LCM of 9 and another number is 45, what is the other number?

Okay, lets begin

Prime factorization of 9: 9=32


LCM = 45 = 32.×5


The other number must have 3 and 5 in its prime factorization, but not more than 31 to keep the LCM as 45.
 

Explanation

Therefore, the missing number is 15.
 

Well explained 👍

Problem 2

A company has meetings every 9 days and 15 days. If both the conference rooms are booked today, when will they next be booked together ?

Okay, lets begin

 LCM(9,15) =45
 

Explanation

The conference rooms will be booked on the same day in 45 days again. The LCM expresses the smallest common time interval between the digits. 
 

Well explained 👍

Problem 3

The ratio of the LCM of 9 and 15 to their GCF is what?

Okay, lets begin

LCM(9,15)=45, GCF(9,15)=3


Ratio = LCM/GCF=45/3=15
 

Explanation

The ratio of the LCM of 9 and 15 to their GCF is 15. 
 

Well explained 👍

FAQs on LCM of 9 and 15

1. What is the LCM of 9,12 and 15?

LCM (9,12,15) = 180. 


180 is the smallest number that appears commonly on the lists of the numbers 9,12 and 15. 
 

2.What is the LCM of 8,9,10,15 and 20?

LCM (8,9,10,15,20) = 360 


360 is the smallest number that appears commonly on the lists of the numbers 8,9,10,15 and 20. 
 

3.What is the HCF of 9,15 and 24?

Factors of 9 are 1,3,9 


Factors of 15 are 1,3,5,15 


Factors of 24 are 1,2,3,4,6,8,12,24 


(9,15,24) = 3 
 

4.What is the LCM of 9,15 and 24?

360 is the smallest number that is commonly on the lists of the numbers 9,15 and 24.

LCM (9,15,24)= 360
 

5. Find the LCM of 9 and 15 using the prime factorization method.

Prime factors of 9 =3×3 


Prime factors of 15 = 3×5 


LCM (9,15) = 3×3×5 = 45
 

Important glossaries on the LCM of 9 and 15

  • Multiple — product of a number and a natural integer 
  • Prime factor — number one gets after prime factorization any given number 
  • Prime factorization — the process of breaking the number into its prime factors. 

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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.