157 LearnersLast updated on May 26th, 2025
LCM of 12 and 28
LCM is the smallest multiple of two numbers. In day to day life, LCM is used for setting alarms, synchronizing traffic lights and making music. In this article, we will learn about the LCM of 12 and 28.
What is the LCM of 12 and 28?
The LCM of 12 and 28 is 84.
Let us learn how to find and apply it.
How to find the LCM of 12 and 28?
We can find the LCM of 12 and 28 using,
- Listing multiples method
- Prime factorization method
- Division method
LCM of 12 and 28 using the Listing multiple method
In this method, we just list down the multiples of the numbers till we land at the first common multiple, which is the smallest multiple or the LCM of the numbers.
In the case of 12 and 28,
12=12, 24, 36, 48, 60,72, 84, 96, 108…
28=28, 56, 84, 112, 140…
LCM(12,28) = 84
LCM of 12 and 28 using the prime factorization method
The numbers are factored, and their highest powers are multiplied to find the LCM Prime factorized of -
12= 2×2×3
28=2x2x7
LCM(12,28) = 84
LCM of 12 and 28 using the division method
Follow these steps to find LCM using this method;
1.Write the numbers in row
2.Proceed with dividing the numbers with a factor that can be divisible by at least one of the numbers.
3.Carry forward the numbers that haven’t been divided earlier
4.Continue division till the remainder is 1
5.Multiply the divisors in the first column to find the LCM
6.LCM (12,28) = 84
Common mistakes and how to avoid them while finding the LCM of 12 and 28
Here are a few common mistakes one is likely to make while trying to find the LCM. One of the common mistakes among students is forgetting to include all the prime factors. The another mistake is just multiplying the numbers will result in correct LCM, which often leads to an error.
Mistake 1
Make confusion of Greatest Common Divisor with LCM
Students have confusion with GCD and LCM and mistakenly find the solution of GCD instead of the LCM.
LCM of 12 and 28 Examples
Problem 1
Basic calculation of LCM of 12 and 28
Step 1: Finding Factorization
12 = 22 × 3
28 = 22 × 7
Step 2: Taking highest power of all prime numbers
LCM = 22 × 3 × 7 = 84
Hence, the LCM of 12 and 28 is 84.
Explanation
find factors of 84 and then multiply highest power of all prime numbers.
Problem 2
The least common multiple of number 12 and another number is 84. One of the numbers is given as 28. Find the missing number?
LCM of 12 and 28 = 84.
Hence, the missing number is 28.
Explanation
As we know that LCM of 12 and 28 should be 84.
Problem 3
To check the Relationship Between LCM and GCD of 12 and 84
LCM (12,28) = 84
GCD(12,28) = 4
LCM (a, b) × GCD(a, b) = a × b
84 × 4 = 12 × 28
336 = 336
Hence, the relationship is proved.
Explanation
formula used :LCM (a, b) × GCD(a, b) = a × b
FAQs for LCM of 12 and 28
1.What is the common factor of 12 and 28?
2.How to find LCM of 12 and 28?
3.What is the LCM of 21 and 28?
4.What is the LCM of 12 and 18?
5.What is the LCM of 28 12 and 16?
6.How can children in Oman use numbers in everyday life to understand LCM of 12 and 28?
7.What are some fun ways kids in Oman can practice LCM of 12 and 28 with numbers?
8.What role do numbers and LCM of 12 and 28 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve LCM of 12 and 28 skills?
Important Glossaries for LCM of 12 and 28
- Multiple: Product of a number and a natural integer.
- Prime Factor : Number one gets after factorization any given number
- Prime factorization Problem: Based Formula
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About BrightChamps in Oman
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.
