152 LearnersLast updated on May 26th, 2025
LCM of 54 and 12
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 -
- Listing Of Multiples
- Prime Factorization
- 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.
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.
Mistake 1
Confusing factors and multiples
Students used to confuse factors and multiples. To avoid confusion, students need to understand the concept of multiples and factors. Multiplies of a number are the product of the number with whole numbers, whereas factors of the number are the numbers which can evenly divide the number. For example, 1, 2, 3, 4, 6, and 12 are the factors of 12; whereas 12, 24, 36, 48, 60,… are the multiples of 12.
LCM of 54 and 12 Example
Problem 1
Find the smallest number that is divisible by 54 and 12 exactly.
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.
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?
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
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?
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
FAQ on LCM of 54 and 12
1.What are the factors of 54 and 12?
2.What is the LCM of 12 and 54?
3.What is the LCM of 54, 12, and 66?
4.What is the LCM of 30 and 35?
5.What is the GCF of 9 and 15?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 54 and 12?
7.What are some fun ways kids in United Kingdom can practice LCM of 54 and 12 with numbers?
8.What role do numbers and LCM of 54 and 12 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve LCM of 54 and 12 skills?
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.
