LCM of 9,12 and 18
2026-02-28 19:07 Diff
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Last updated on August 5, 2025

LCM is applied in most everyday tasks like planning, aligning events and even in alarms which is used literally every day. In this article, let us learn more about the LCM of 9,12 and 18.

What is the LCM of 9,12 and 18?

The LCM of 9,12 and 18 is 36. How did we find this?
Let us learn!
 

How to find the LCM of 9,12 and 18?

LCM of 9,12 and 18 using the Division method

In this method, we list the multiples of the numbers given until we land at the smallest multiple that is common between the numbers. 


To elaborate; 


Multiples of 9 = 9,18,27,36,…


Multiples of 12 = 12,24,36,…


Multiples of 18 = 18,36,...


From the above we can clearly see that the smallest common multiple between the numbers is 36, which is the LCM of 9,12 and 18. 


LCM (9,12,18) = 36 
 

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LCM of 9,12 and 18 using the prime factorization method

Here, we factorize the numbers into their prime factor and multiply the highest powers to find the LCM. 


Substantiating the above; 


Step 1. Prime factorize the numbers,


9 = 3×3


12 = 2×2×3


18= 2×3×3


Step 2. Multiply the highest powers 


Step 3. Multiply the factors to get the LCM 


LCM(9,12,18) = 36
 

LCM of 9,12 and 18 using the division method

In the division method, 


Step 1: Write the given numbers in a row 


Step 2: proceed with the division of numbers with a factor that is divisible by at least one of the numbers. 


Step 3: Carry forward the numbers that haven’t been divided earlier. 


Step 4: Continue dividing till the remainder is 1 for all the numbers. 


Step 5: Multiply the divisors in the first column to find the LCM. 


Step 6: LCM (9,12,18) = 36 
 

Common mistakes and how to avoid them in LCM of 9,12 and 18

Listed here are a few common mistakes that one may commit while trying to find the LCM of 9,12 and 18, make a note while practicing. 

Problem 1

LCM(9,12) = 36, LCM (9,12,x) is also 36. Find x.

Okay, lets begin

The possible values of x could be → 1,2,3,4,6,9,12,18 or 36. 
 

Explanation

The LCM of the numbers 9 and 12 is 36 and for the LCM to still remain as 36 after a number is included, i.e., 9,12,x; it must be a divisor of the number 36. The possible number of x is going to be a divisor of 36. Therefore, the possible values could be the above listed divisors. 

Well explained 👍

Problem 2

Find x, LCM (99,12,x) = 36.

Okay, lets begin

We know the LCM of 9,12 = 36 


Prime factorization of 36 36 = 3×3×2×2 


The LCM of 3,9 already includes 32 and 22, and the factor of x must include the same, which means the factors of 36 are likely the value of x → 1,2,3,6,12,18,36. 
 

Explanation

By following the above assumption we can assume that the value of x is one of 1,2,3,6,12,18,36. 
 

Well explained 👍

Problem 3

Prove that LCM(a², b²) = LCM(a, b)² in a case where ‘a’ and ‘b’ are co-prime. Apply to find the LCM(9²,12²).

Okay, lets begin

We can tell that 9 and 12 are not coprime, they have more factors than just 1 and themselves. To make it so, we prime factorize them; 


9 = 32


12 = 22×3 


Now we find their squares; 


92 = 34 = 81


122 =24×32 = 144


We now use the formula for prime factors; 


LCM(92,122) = LCM(34,24×32) 


= 24×34 


= 16×81 


= 1296
 

Explanation

The formula LCM(a2, b2) = LCM(a, b)2 holds good. The LCM of 92 and 122 is 1296.
 

Well explained 👍

FAQs on the LCM of 9,12 and 18

1.What is the LCM of 9,12,18,36?

Prime factorize the numbers;


9 = 3×3


12 = 2×2×3


18 = 3×3×2


36 = 2×2×3×3 


LCM(9,12,18,36) = 36 
 

2.What is the LCM of 9,12,18, 24 and 27?

Prime factorize the numbers; 


9 = 3×3


12 = 2×2×3


18 = 3×3×2


24 = 2×2×3×2 


27= 3×3×3


LCM(9,12,18,24,27) = 648
 

3.What is the HCF of 9,12,18 and 21?

List the common factors of the numbers given;


Factors of 9 = 1,3,9 


Factors of 12 = 1,2,3,4,6,12


Factors of 18 = 1,2,3,6,9,18


Factors of 21 = 1,3,7,21


HCF(9,12,18,21) = 3 
 

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

Prime factorize the numbers; 


9 = 3×3


12 = 2×2×3


15 = 3×5


LCM (9,12,15) = 180 
 

5.What is the GCF of 15 and 60?

List the common factors of the numbers given; 


Factors of 15 = 1,3,5,15


Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60 


HCF(15,60) = 15 
 

Important glossaries for the LCM of 9,12 and 18

  • Multiple — It is a product of a number and any natural integer. So for 18; 18,36,54 are the multiples.
  • Prime Factor — It is a prime number that one gets after factorization of any given number. Like for 12; 1,2,3,4,6 and 12 are prime factors as they can be divided by 1 or the number itself.
  • Prime Factorization — It is a process of dividing the number into prime factors.
  • Co-prime numbers — These are the positive integers, where both the numbers can be divided only by 1. 
  • Fraction — It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 18/9– 18 is the numerator and 9 is the denominator. Proper fraction is where numerator is always lesser than denominator.
     

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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.