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Last updated on May 26th, 2025

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LCM Of 6, 12 and 15

Professor Greenline Explaining Math Concepts

The Least Common Multiple (LCM) is the smallest number that when we divide by two or more numbers at a time, all three or more numbers divide into it. LCM also helps in math problems and everyday things like event planning or buying supplies. We will find the LCM of 6, 12 and 15 together and what that really means.

LCM Of 6, 12 and 15 for Qatari Students
Professor Greenline from BrightChamps

What Is The LCM Of 6, 12 And 15?

The LCM or the least common multiple of 2 numbers is the smallest number that appears as a multiple of both numbers. In case of 6, 12 and 15, The LCM is 60. But how did we get to this answer? There are different ways to obtain a LCM of 2 or more numbers. Let us take a look at those methods.
 

Professor Greenline from BrightChamps

How To Find The LCM Of 6, 12 And 15

Remember that we previously said there are plenty of ways to calculate the LCM of two numbers or more. Then some of those methods make it extremely easy for us to find the LCM of any two numbers. Those methods are: 

 

  • Listing of Multiples

 

  • Prime Factorization

 

  • Division Method

 

Finally, now we will learn how each of these methods can help us to calculate LCM of given numbers.
 

Professor Greenline from BrightChamps

Finding LCM Of 6, 12 And 15 By Listing Of Multiples

This method will help us find the LCM of the numbers by listing the multiples of the given numbers. Let us take a step by step look at this method.


The first step is to list all the multiples of the given numbers.


Multiples Of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60.


Multiples Of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120.


Multiple Of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150.


The second step is to find the smallest common multiples in both the numbers. In this case, that number is 60 as highlighted above.


By this way we will be able to tell the LCM of given numbers.
 

Professor Greenline from BrightChamps

Finding The LCM By Prime Factorization

Let us break down the process of prime factorization into steps and make it easy for children to understand.
The first step is to break down the given numbers into its primal form. The primal form of the number is:


6= 3×2


12= 2×2×3


15= 5×3


As you can see, 2 appears as a prime factor in both numbers. So instead of considering 2 five times, we will only consider it four times. So the final equation will look like (2×2×3×5).


So after the multiplication, we will be getting the LCM as 60.


As you can see, using this method can be easier for larger numbers compared to the previous method. 
 

Professor Greenline from BrightChamps

Finding The LCM By Division Method

The method to calculate the LCM is really simple. We’ll break these given numbers apart till it comes down to one, by dividing it by the prime factors. The product of the divisors that will come is the LCM of the given numbers.


Let us understand it step by step:


The first thing is to find the number common in both the numbers. Here it is 3. In that case, we divide the numbers by 3. It will reduce the values of the numbers to 2, 4 and 5.


5 is a prime number, it can be divided by only 5. That means after dividing, there will be only 2 and 4 left. This can be divided by 2 which will bring 4 down to 2 and 2 will be reduced to 1. As 2 is a prime number, it can only be divided by 2. After this step, there will only be 1’s left in the last row.


This is the end of division. However, we will now find the product of the numbers on the left. The numbers on the left side are: 2,2,3 and 5. 


These numbers multiplied give 60. On this basis, therefore, the LCM of the 6, 12 And 15 becomes 60.
 

Max Pointing Out Common Math Mistakes

Common Mistakes And How To Avoid Them For LCM Of 6, 12 And 15.

Let us look at some of the common mistakes that can happen while solving a given assignment regarding LCM.
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Missing a prime factor,
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
 

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LCM Of 6,12 And 15 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

If a train arrives every 6 minutes, 12 minutes, and 15 minutes, when will they arrive together?

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 The trains will arrive together every 60 minutes.

Explanation

To find when the trains meet, we look for the smallest number that 6, 12, and 15 can all divide into, which is 60.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

Sam’s friends come every 6, 12, and 15 days. When will they all come together again?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

 They will meet every 60 days.
 

Explanation

To find when they all meet, find the least common multiple (LCM) of 6, 12, and 15. The LCM is 60, so they meet in 60 days.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Lily cycles every 6 days, Tim every 12, and Max every 15. When will they cycle together?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

They will cycle together every 60 days.

Explanation

 Lily cycles every 6 days, Tim every 12, and Max every 15. The smallest number they all share is 60, so they cycle together every 60 days.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

Three singers sing every 6, 12, and 15 days. When do they sing together?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

They will all sing together again in 60 days.
 

Explanation

To find when they sing together, we find the smallest number that 6, 12, and 15 divide into. That number is 60.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

If three friends walk every 6, 12, and 15 minutes, when do they meet again?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

They meet every 60 minutes.
 

Explanation

The three friends walk every 6, 12, and 15 minutes. They will all meet together again after 60 minutes because 60 is the smallest time that divides evenly by 6, 12, and 15.
 

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs For LCM Of 6,12 And 15

1.What is the smallest common multiple of 6, 12, and 15?

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2.What is the difference between GCD and LCM of 6, 12, and 15?

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3.Can LCM be found using prime factors?

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4.What is the LCM of 1 and any number?

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5.What if there are no common multiples?

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6.How can children in Qatar use numbers in everyday life to understand LCM Of 6, 12 and 15?

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7.What are some fun ways kids in Qatar can practice LCM Of 6, 12 and 15 with numbers?

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8.What role do numbers and LCM Of 6, 12 and 15 play in helping children in Qatar develop problem-solving skills?

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9.How can families in Qatar create number-rich environments to improve LCM Of 6, 12 and 15 skills?

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Professor Greenline from BrightChamps

Important Glossaries for LCM of 6,12 and 15

  • Least Common Multiple (LCM): The smallest number that can be evenly divided by two or more numbers. It helps in solving problems involving groups or schedules.

 

  • Factor: A number that divides another number evenly (e.g., 1, 2, and 3 are factors of 6).

 

  • Prime Factorization: Breaking a number down into its prime factors. For example, the prime factorization of 12 is 2 × 2 × 3.

 

  • Prime Factorization: Breaking a number down into its prime factors. For example, the prime factorization of 12 is 2 × 2 × 3.
Professor Greenline from BrightChamps

About BrightChamps in Qatar

At BrightChamps, numbers represent more than digits—they unlock countless opportunities! Our goal is to help children throughout Qatar master important math skills, focusing on the LCM Of 6, 12 and 15 with special attention on understanding the LCM—in a lively, fun, and easy way. Whether your child is calculating how fast a roller coaster moves at Qatar’s Angry Birds World, keeping score at local football matches, or managing their allowance to buy gadgets, mastering numbers builds confidence for daily challenges. Our interactive lessons make learning enjoyable and simple. Because children in Qatar learn in many different ways, we adapt our approach to suit each learner. From Doha’s modern cityscape to desert landscapes, BrightChamps makes math come alive. Let’s make the LCM a fun part of every child’s learning!
INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
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USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom