156 LearnersLast updated on May 26th, 2025
LCM of 5, 9, and 15
Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers. By learning the following tricks, you can learn the LCM of 5, 9, and 15 easily.
What Is the LCM of 5, 9, and 15?
The LCM of 5, 9, and 15 is 45. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
How to find the LCM of 5, 9, and 15?
We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:
Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method
Now let us delve further into these three methods and how it benefits us.
LCM of 5, 9, and 15 Using Listing of Multiples Method
In this method, we will list all the multiples of 5, 9, and 15. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50,....
Multiples of 9:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90,...
Multiples of 15:
15, 30, 45, 60, 75, 90, 105,...
The LCM of 5, 9, and 15 is 45. 45 is the smallest number which can be divisible by all 5, 9, and 15.
LCM of 5, 9, and 15 Using Prime Factorization
To find the LCM of 5, 9, and 15 using the prime factorization method, we need to find out the prime factors of the numbers. Then multiply the highest powers of the factors to get the LCM.
Prime Factors of 5 are: 51.
Prime Factors of 9 are: 32.
Prime factors of 15 are: 31, 51
Multiply the highest power of all the factors: 32 × 51 = 3 × 3 × 5 = 45
Therefore, the LCM of 5, 9, and 15 is 45.
LCM of 5, 9, and 15 Using Division Method
To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.
For finding the LCM of 5, 9, and 15 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 5, 9, and 15.
3 × 3 × 5 = 45
The LCM of 5, 9, and 15 is 45
Common Mistakes and How to Avoid Them in LCM of 5, 9, and 15.
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
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 5,9 and 15 Examples
Problem 1
In a class, every 5th student gets a 10% scholarship, every 9th student gets a 15% scholarship, and every 15th student gets a 20% scholarship. Out of 100 students, how many students receive multiple scholarships, and what is the minimum percentage they receive?
Prime factorization: 5 = 5, 9 = 32, 15 = 31 × 51
LCM is 32 × 5 = 45
Every 45th student qualifies for scholarships in all three categories.
Since there are 100 students, 100 / 45 = 2
Therefore, 2 students will receive multiple scholarships
The minimum percentage a student in this group would receive is 10% + 15% + 20% = 45%
Explanation
We determined the LCM of 5, 9, and 15 to find the frequency at which students overlap in receiving multiple scholarships. Then, we used this result to see how many students out of 100 met this criterion and calculated the minimum percentage they would receive.
Problem 2
Three machines A, B, and C produce a certain part every 5, 9, and 15 minutes, respectively. If they all start production at the same time, how often will they all finish a part simultaneously in a day?
LCM (5,9,15) = 45
So, the three machines will work together for every 45 minutes.
Explanation
To find the time when three machines work together we find the LCM of 5, 9, and 15.
Prime factorization of 5 = 51
Prime factorization of 9 = 32
Prime factorization of 15 = 31 × 51
LCM (5, 9, 15) = 32 × 51
= 9 × 5 = 45
Problem 3
If the LCM of three numbers is used to find the frequency of occurrence in an event, derive the number of occurrences if the intervals are 5, 9, and 15 minutes during the day.
LCM (5,9,15) = 45
Total time in minutes for 24 hours = 24 × 60 = 1440 minutes.
Frequency of occurrence: 1440 / 45 = 32
Explanation
Using the LCM as the interval at which the event repeats, we divide the total time (1440 minutes) by 45 to find the number of times all events align in 24 hours.
FAQs on the LCM of 5,9 and 15
1.What are the first five common multiples of 9 and 15?
2.What is the GCF of 5, 9, and 15?
3. What is the LCM of 9, 10, and 15?
4.What is the LCM of 5,9 and 15?
5. What is the LCM of 6,9 and 15?
6.How can children in Qatar use numbers in everyday life to understand LCM of 5, 9, and 15?
7.What are some fun ways kids in Qatar can practice LCM of 5, 9, and 15 with numbers?
8.What role do numbers and LCM of 5, 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 5, 9, and 15 skills?
Important glossaries for the LCM of 5,9 and 15
- Prime Number: Any number that has only 2 factors is called a prime number.For example, 5 and 7, only common factors are 1 and the number itself.
- Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8, and 10.
- Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
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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.
