LCM of 6,9 and 12
2026-02-28 09:57 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 6,9 and 12. 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 6,9 and 12?

How to find the LCM of 6,9 and 12?

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

LCM of 6,9 and 12 using the Listing Multiples Method

The LCM of 6,9 and 12 can be found using the following steps:


Step 1: Write down the multiples of each number


Multiples of 6  = 6,12,…36,…


Multiples of 9 = 9,18,…,36,…


Multiples of 12 = 12,…,36,…


Step 2:   Ascertain the smallest multiple from the listed multiples


The smallest common multiple is 36


Thus, LCM (6,9,12) = 36

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LCM of 6,9 and 12 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 the numbers:


Prime factorization of 6 = 2×3


Prime factorization of 9 = 3×3


Prime factorization of 12 = 2×3×2

Step 2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:


 2×3×2×3 = 36


        LCM(6,9, 12) = 36
 

LCM of 6,9 and 12 using the Division Method

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

Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

2×2×3×3= 36

Common Mistakes and how to avoid them in LCM of 6,9 and 12

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6,9 and 12, make a note while practicing.
 

Problem 1

Runner A runs every 9 minutes in a trail and runner B every 12 minutes and runner C runs every 6 minutes, and both of them start together. When will they both meet at the starting point again?

Okay, lets begin

The LCM of 6,9 and 12 is 36.
 

Explanation

Runner A and B will meet at the starting point in 36 minutes, the LCM of 6,9 and 12 is 36, which is the smallest common time interval for the given digits. 
 

Well explained 👍

Problem 2

List the smallest number that is divisible by 6,9 and 12.

Okay, lets begin

The LCM of 6,9 and 12 is 36. 
 

Explanation

The LCM of 6,9 and 12 is 36, which is the smallest number divisible by given digits

Well explained 👍

Problem 3

Workers A, B and C complete a task every 6 days, 9 days and 12 days respectively. If they start working together now, when will they complete the task if they work at their respective rates ?

Okay, lets begin

Find the total work done per day by workers A, B and C, i.e., the sum of individual work rates; 


Worker A = 1/6


Worker B = 1/9


Worker C = 1/12 


Calculate the LCM of the denominators,


Prime factorization of 6 = 2×3


Prime factorization of 9 = 3×3


Prime factorization of 12 = 2×3×2


LCM (6,9,12) = 36


By finding the LCM, we find a common period for comparison, contribution of workers A, B and C over 36 days are; 


Worker A = 36/6 = 6


Worker B = 36/9 = 4

Worker C = 36/12 =3


Together, A, B and C complete 13 (6+4+3) tasks every 36 days. 


Time to complete 1 task by all the 3 workers = 36/13 = 2.769 
 

Explanation

In 2.769 days, workers A, B and C will complete their task.
 

Well explained 👍

Problem 4

The math teacher hands an assignment every 2 days and the science teacher every 9 days and English teacher every 6 days. If both the assignments are due today, when will the students be due to turn in their assignments next on the same day?

Okay, lets begin

The LCM of 6,9 and 12 is 36. 
 

Explanation

The math, English, and science assignments will be due again together in 36 days, the LCM of 6,9 and 12 is 36, which is the smallest common time interval for the given digits. 
 

Well explained 👍

FAQs on LCM of 6,9 and 12

1.What is the LCM of 6,9,12 and 18?

Prime factorization of 6 = 2×3


Prime factorization of 9 = 3×3


Prime factorization of 12 = 2×3×2


Prime factorization of 18 = 3×3×2


LCM (6,9,12,18) = 36 
 

2.What is the LCM of 3,6,9 and 12?

Prime factorization of 3 = 3 


Prime factorization of 6 = 2×3


Prime factorization of 9 = 3×3


Prime factorization of 12 = 2×3×2


LCM (3,6,9,12) = 36 
 

3.Is 12 divisible by 9?

No, 12 is not divisible by 9. When divided, it leaves a remainder. 
 

4.What is the LCM of 9 and 12?

Prime factorization of 9 = 3×3


Prime factorization of 12 = 2×3×2


LCM (9,12) = 36 
 

5.What is the LCM of 6,9 and 10?

Prime factorization of 6 = 2×3


Prime factorization of 9 = 3×3


Prime factorization of 10 = 2×5 


LCM (6,9,10) = 90
 

Important glossaries for the LCM of 6,9 and 12

  • 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.