158 LearnersLast updated on May 26th, 2025
LCM Of 3,9 and 15
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 3,9, and 15 together and what that really means.
What Is The LCM Of 3,9 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 3,9 and 15, The LCM is 45. 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.
How To Find The LCM Of 3,9 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.
Finding LCM Of 3,9 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.
Step 1: list all the multiples of the given numbers.
Multiples Of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57 and 60.
Multiples Of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81 and 90.
Multiples Of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135 and 150.
Step 2: find the smallest common multiples in both the numbers. In this case, that number is 45 as highlighted above.
By this way we will be able to tell the LCM of given numbers.
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.
Step 1: break down the given numbers into its primal form. The primal form of the number is:
3= 3
9= 3×3
15= 3×5
Step 2: As you can see, 3 appears as a prime factor in all three numbers. So instead of considering 3 4 times, we will only consider it two times. So the final equation will look like (3×3×5).
So after the multiplication, we will be getting the LCM as 45.
As you can see, using this method can be easier for larger numbers compared to the previous method.
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 1, 3 and 5.
As 3 and 5 are prime numbers, we will divide those numbers by themselves and get the last to be only 1’s.
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:3,3 and 5.
These numbers multiplied give 45. On this basis, therefore, the LCM of the 3,9 and 15 becomes 45.
Common Mistakes That Are Made And How To Avoid Them For LCM Of 3,9 and 15
Let us look at some of the common mistakes that can happen while solving a given assignment regarding LCM.
Mistake 1
Missing a prime factor
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
LCM Of 3,9 And 15 Examples
Problem 1
Anna practices violin every 3 days, Sam every 9 days, and Lily every 15 days. When will they practice together?
Anna, Sam, and Lily will practice together in 45 days.
Explanation
45 is the smallest number that can be divided evenly by 3, 9, and 15. This means they will all practice together in 45 days.
Problem 2
A school has gym days every 3 days, art days every 9 days, and science days every 15 days. When will all fall on the same day?
All activities will happen together in 45 days.
Explanation
The smallest number that 3, 9, and 15 can divide evenly is 45, so that's when all three activities will be on the same day.
Problem 3
Amir fills the tank every 3 days, Sue every 9 days, and Jake every 15 days. When will they refill together?
They will refill together in 45 days.
Explanation
The smallest number of days that work for all their schedules is 45. This is called the “least common multiple” (LCM) of 3, 9, and 15.
Problem 4
Workers get breaks every 3, 9, and 15 days. When will they break on the same day?
In 45 days, the workers will all take a break on the same day.
Explanation
The smallest number that 3, 9, and 15 divide into evenly is 45, so they’ll all rest together after 45 days.
Problem 5
Three friends visit a park every 3, 9, and 15 days. When will they all meet up again?
They’ll meet again in 45 days.
Explanation
The smallest number that 3, 9, and 15 all divide into evenly is 45. So, after 45 days, all three friends will meet again
FAQs For LCM 3,9 and 15
1.What is the GCF of 3,9 and 15?
2.What is the LCM of 5,9,15 and 3?
3.What is the LCM of 9 and 15?
4.What is the LCM of 3 and 15?
5.What is the LCM of 3,9 and 15?
6.How can children in Qatar use numbers in everyday life to understand LCM Of 3,9 and 15?
7.What are some fun ways kids in Qatar can practice LCM Of 3,9 and 15 with numbers?
8.What role do numbers and LCM Of 3,9 and 15 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM Of 3,9 and 15 skills?
Important Glossaries for LCM of 3,9 and 15
- LCM (The Least Common Multiple): The smallest number that can be evenly divided by two or more numbers without leaving a remainder.
- Multiple: A number that can be obtained by multiplying a given number by an integer. For example, multiples of 3 include 3, 6, 9, 12, etc.
- Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, etc.
- Division Method: A technique to find the LCM by dividing the given numbers by their common prime factors until only 1s remain.
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About BrightChamps in Qatar
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.
