LCM of 15 and 27
2026-02-28 09:52 Diff
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Last updated on August 5, 2025

The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.

What is the LCM of 15 and 27?

We use LCM of 15 and 27 to find  the smallest number that divides both the numbers equally.  The smallest positive number is the number that divides both numbers equally, is 210 without leaving any remainder. LCM is used mainly in fractions to find a common number for both the integers.
  

How to find the LCM of 15 and 27?

LCM of 15 and 27 using Division method:

In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime factors and identify them.

  • 3 divides 15 and 27
  • 5 divides 15 and not 27
  • 9 divides 27 and not 15

Now multiply the divisors : 3×5×9=135 which is the LCM.
 

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LCM of 15 and 27 using Listing multiples:

Start by listing multiples of both the numbers separately:


Multiples of 15 are 15,30,45,60,75,90,105,120,135…..


Multiples of 27 are 27,54,81,108,135…..

The least common factor from the list is 135. Therefore, the LCM of 15 and 27 is 135.
 

LCM of 15 and 27 using Prime factorization:

We part both the numbers unto factors:


Factor of 15: 3×5


Factors of 27: 33

Take the powers of both the numbers and multiply together:


LCM=33x5=135.
 

Common Mistakes and How to Avoid Them in LCM of 15 and 27

While solving problems based on the LCM of 15 and 27, children fail to understand few concepts, to give an idea of the mistakes, given below are a few mistakes and solutions of how to avoid them:
 

Problem 1

Find the LCM of 15 and x, if the LCM is 60. What is the value of X?

Okay, lets begin

X=4.

Explanation

To add the fractions, we need to find the prime factorization of 15


 Prime factors of 15: 3 × 5


The LCM of 15 and X is given as 60.


 60= 22 x3x5

Since X shares factors with 60, the  missing number should include 22 as 15 does not include any factor of 2.

Therefore, 


X=22=4.

LCM of 15 and 4 is : 


LCM(15,4)= 22  × 3 × 5 =60.

Thus, X=4.
 

Well explained 👍

Problem 2

Given two pairs of numbers (12,18) and (15,24) which pair has the greater LCM?

Okay, lets begin

let us first find LCM of each pair:


LCM of 12 and 18: 


Factorization of 12= 22  × 3


Factors of 18= 2x 32


Take the highest powers of both the numbers:


LCM(12,18)= 22 × 32 = 4 × 9=36

LCM of 15 and 24:


Factorization of 15= 3 × 5


Factorization of 24= 23 × 3


Take the highest powers of both the numbers:


LCM(15,24)= 23 × 3 × 5= 8 × 15=120.
 

Explanation

LCM(15,24)= 120

LCM(12,18)= 36

so, (15,24 has greater LCM

Well explained 👍

Problem 3

Simplify the fraction 15/27 by finding the LCM of the numerator and the denominator’s greatest common divisor(GCD).

Okay, lets begin

answer : 5/9

Explanation

Prime Factorization of 15:


15=3 × 5

Prime Factorization of 27:


27=33

GCD of 15 and 27 is 3.

To simplify: 


15/27 = 15÷3/27÷3 = 5/9.

Well explained 👍

Problem 4

If the LCM of two numbers a and b is 72, and their GCD is 4. Find the product of a and b.

Okay, lets begin

product of a and b =288

Explanation

LCM(a, b) x GCD (a, b)= a × b


LCM(a, b)=72 and GCD(a, b)=4


72 × 4= a × b


a × b =288.

Well explained 👍

Problem 5

If a=18 and LCM of a and b is 90, find b.

Okay, lets begin

b=10.

Explanation

 by using the formula:


LCM(a, b)= a × b/GCD(a, b)

18=2x32 and the LCM is 90


Factors of 90 are 2 × 32 × 5


The missing factor is 5, so b =5 × 2 =10


b=10.

Well explained 👍

FAQs on LCM of 15 and 27

1.What is the LCM of 18 and 27?

The LCM of 18 and 27 is 54. To find the LCM of 18 and 27.

Multiples of 18 = 18,36,54,72;


Multiples of 27= 27,54,81,108.


The LCM of 18 and 27 is 54.

2.There are how many factors in 3600?

There are 45 factors of 3600, but the prime factors are 2,3,5.
 

3.Write the LCM of 15,18,24,27 and 56 ?

The LCM of 15,18,24,27 and 56 is 7560.

4.What is the LCM of 8,14 and 9?

 8=23


14=2x7


9=32


8x7x9=504
 

5.If the LCM of two numbers a and b is 840, and one of the numbers is 28, find the smallest possible value of b?

LCM(a, b)= a x b/GCD(a, b)


a=28 and LCM(a, b)=840


2x3x5=30.
 

Important glossaries on the LCM of 15 and 14

  • Prime Factor: A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2×7.
  • Co-prime numbers: numbers which have the only positive divisor of them both as 1. For example, 6 and 7.
     

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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.