LCM of 54 and 12
2026-02-28 18:02 Diff
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Last updated on August 5, 2025

LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, and distributing any items among others. In this topic, we will learn more about LCM of 54 and 12.

What is the LCM of 54 and 12

The common multiples of 54 and 12 is 108.  Here, we will learn about the LCM of 2 numbers. Children learn about LCM at younger ages. Here, we will discuss the methods used for finding out LCM.
 

How to find the LCM of 54 and 12?

Out of many methods, prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows - 

  1. Listing Of Multiples
  2. Prime Factorization
  3. Division Method
     

LCM of 54 and 12 Using Listing the Multiplies

Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 2 numbers is noted - 

  • Multiples of 54: 54, 108, 162, 216
  • Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108

Then we can see that out of 54 and 12, 108 is the smallest common number that is present in them. So we see that 108 is the LCM of 54 and 12. 
 

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LCM of 54 and 12 Using Prime Factorization

The product of the highest power of prime factors of 54 and 12 is the LCM of these numbers. So let us look at it step by step to understand it better.


Breaking the given numbers into their prime factors.


Prime factorization of 54: 2 × 3 × 3 × 3


Prime factorization of 12: 2 × 2 × 3 


Multiplying the highest power of prime factors: 22 × 33  → 4 × 27 = 108


LCM of 54 and 12 is 108.
 

LCM of 54 and 12 Using Division Method

In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.

Step 1: Arrange the number in a sequence, divisors, and the numbers are on the left and right sides respectively.


Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 54 and 12 by 2. The result is 27 and 6. 


Step 3: As 6 is divisible by 2, again the divisor is 2. Dividing 27 and 6 by 2. Now the result is 27 and 3.


Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.

The divisors are 2, 2, 3, 3, 3. LCM of 54 and 12 is the product of divisors.


Hence, the LCM of (54 and 12) = 2 × 2  × 3 × 3 × 3 = 108
 

Common Mistakes and How to Avoid Them in LCM of 54 and 12

There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.

Problem 1

Find the smallest number that is divisible by 54 and 12 exactly.

Okay, lets begin

By using a listing multiples method: 


Multiples of 54 and 12:
Multiples of 54: 54, 108,162
Multiple of 12: 12, 24, 36, 48, 60, 72, 84, 108


Here, the LCM of 54 and 12 is 108
 

Explanation

So we get the LCM of 54 and 12 is 108. That means the smallest number that both 54 and 12 can divide into perfectly.
 

Well explained 👍

Problem 2

Two machines are set to beep at intervals of 54 minutes and 12 minutes, respectively. If both machines beep at 10: 00 AM. When will they next be together?

Okay, lets begin

Calculate LCM : 
Prime factor of 54: 2 × 3 ×  3 × 3 
Prime factor of 12: 2 × 2 × 3 
Find the highest power and multiply together.
After multiplying, we get 2 2  × 3 3   = 4 × 27  =108
 

Explanation

The machines will next beep together at 11:48. AM
 

Well explained 👍

Problem 3

A school bus schedule repeats every 54 minutes, and a community bus schedule repeats every 12 minutes. If they both arrive at a stop at 7: 00 AM. When is the next time they will arrive together?

Okay, lets begin

Take the highest power of both prime factors: 


12 = 22
 54= 33


 Then multiply the highest power:


LCM = 22  × 3 3  = 4 × 27 =108
 

Explanation

 Both arrive at 7:OO am, so we simply add 108 minutes to 7: 00 am. Then the next time both buses will arrive together is 8:48 a.m

Well explained 👍

FAQ on LCM of 54 and 12

1.What are the factors of 54 and 12?

 Here, there are several factors: 54 and 12.   The common factors of 54 and 12, 1, 2, 3, 6, 9, 18, 27, 54. Therefore, the greatest common factor of both numbers (54 and 12 is 6)
 

2.What is the LCM of 12 and 54?

 The LCM of 12 and 54 is 108.  The steps of continuous division are, to write the number and divide by the smallest prime numbers, and finally multiply the divisors. 

3.What is the LCM of 54, 12, and 66?

 The Least common multiple of 54, 12, and 66 is 1188. There are only two steps to finding the LCM. First, write the multiple, and second, identify the smallest one. That is divisible by both three numbers. (54, 12, and 66. )
 

4.What is the LCM of 30 and 35?

 The LCM of both numbers is 210. 210 can be exactly divisible by 30 and 35.

5.What is the GCF of 9 and 15?

The term HCF is also known as GCF. So 3 is a larger number than 1. So the GCF of 9 and 15 is 3.
 

Important Glossaries of LCM of 54 and 12

  • Factor: A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.
  • Prime Factorization: When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.
  • Greatest Common Factor (GCF): GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.
  • Division Method: In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1. 
     

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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.