LCM of 15 and 45
2026-02-28 17:14 Diff
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Last updated on August 5, 2025

The LCM or Least Common Multiple of 15 and 45 is the smallest number which can be exactly divisible by each of 15 and 45. It can also be defined as the least number, which is a common multiple of all 15 and 45. LCM helps in scheduling, also used in traffic light mechanisms, etc.

What is the LCM of 15 and 45

The LCM of 15 and 45 is 45. So, 45 is the smallest multiple shared by the numbers 15 and 45. We can get the exact value of LCM of 15 and 45 through various methods. Let us see how.
 

How to find the LCM of 15 and 45

To find the LCM of 15 and 45 we will learn some methods: 

  • Listing Method
  • Prime Factorization Method
  • Division Method
     

LCM of 15 and 45 Using Listing the Multiples

Step 1:List down the multiples of each number


Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,...


Multiples of 45= 45,90,135,180,225,315,....


Step 2: Find out the smallest multiple from the listed multiples


The smallest common multiple is 45


Thus, LCM (15,45) = 45.
 

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LCM of 15 and 45 Using Prime Factorization

Rule: The prime factorization of each number is to be done, and then the highest power of the prime factors are multiplied to get the LCM.

Step 1: Find the prime factorization of the numbers:


 Prime factorization of 15 = 3×5

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


LCM (15,45) = 45.


 Prime factorization of 45 = 5×32
 

LCM of 15 and 45 Using Division Method

This is the most used method to find any LCM. It involves dividing both numbers 15 and 45 by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.


Step 1: Write the numbers, divide by common prime factors. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers


The first common prime divisors for both 15 and 45 are 3 and 5. We choose 5.Step 2: Dividing 15 and 45 with 5, we get 3 and 9 respectively.

Step 3: Repeat Step 1 and 2 till both are getting perfectly divided. 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.

 5×3×3 =  45


Thus, LCM (15,45) = 45

Common Mistakes and How to Avoid Them in LCM of 15 and 45

Misconception is normal, but we should avoid it whenever we are solving math problems. Let us see how we can avoid some common errors.
 

Problem 1

The LCM of 15 and 45 is 45. Then what will be the LCM of 15 and 60?

Okay, lets begin

Prime Factorization of 15 =3×5


Prime Factorization of 60 =5×3×22


LCM(15,60)= 22×3×5 =60
 

Explanation

Solved the LCM of 15 and 45 through Prime Factorization method.
 

Well explained 👍

Problem 2

LCM (15,45) = x. Find the smallest positive integer (n), where n×x=90.

Okay, lets begin

LCM (15,45) = x 


We know that the LCM of 15 and 45 from the previous calculations. 


LCM (15,45) = 45


n×45=90


⇒ n=90 /45


⇒ n = 2


Answer: 2
 

Explanation

 We made use of the LCM OF 15 and 45 and solved the equation to get the value of n.
 

Well explained 👍

Problem 3

What is the LCM of 12, 18 and 15?

Okay, lets begin

 Prime Factorization of 12 =22×3


Prime Factorization of 18 =2×32


 Prime Factorization of 15 =3×5


LCM (12,15,18)= 22×32×5 =180


Answer: 180
 

Explanation

The LCM of numbers 12,15 and 18 are found using the Prime factorization method.
     

Well explained 👍

FAQs on LCM of 15 and 45

1.What is the LCM of 5 and 45?

 Prime Factorization of 5 =5×1


Prime Factorization of 45 =5×32


LCM(5,45)= 5×32 =45

2.What is the LCM of 12,15, and 45?

 Prime factorization of 12 = 22×3


Prime factorization of 15 = 5×3


Prime Factorization of 45 =5×32

LCM (12,15,45) = 32×22×5 = 180
 

3.How to calculate LCM quickly?

Applying the division method, you can find LCM quickly.
 

4.How to calculate LCM?

 LCM can be found through prime factorization or division method mostly.

5.What is the LCM of 20,25 and 30?

Prime factorization of 20 = 5×2×2


Prime factorization of 25 = 5×5


Prime factorization of 30 = 5×2×3 


LCM (20,25,30) = 300
 

Important glossaries for the LCM of 15 and 45

  • Prime Factor: A natural number or whole number which has factors that are 1 and itself.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 
  • Co-prime numbers: numbers which have the only positive divisor of them both as 1. 
  • Relatively Prime Numbers:     Numbers that have no common factors except 1.
  • Multiples: The product we get when all the integers are multiplied with a particular number, one by one.
     

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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.