168 LearnersLast updated on May 26th, 2025
LCM of 4 and 12
LCM is a common multiple, the smallest value between the numbers 4 and 12. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.
What is the LCM of 4 and 12?
The LCM of 4 and 12 is 12. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below.
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LCM of 4 and 12 Using Listing the Multiples
Step 1: Write down the multiples of the numbers. Don’t stop too early.
— Multiples of 4 = 4,8,12,16,20,24, …
— Multiples of 12 = 12, 24, 46, …
Step 2: Find the smallest number common between the written multiples of 4 and 12
— The smallest common multiple is 12
Thus, LCM(4,12) = 12
LCM of 4 and 12 Using Prime Factorization
Step1 : factorize the numbers into its prime factors
4 = 2 × 2
12 = 2 × 2 × 4
Step 2: find the highest powers of the factors of 4 and 12
Step 3:Multiply the highest powers
LCM(4,12) = 12
LCM of 4 and 12 Using Division Method
- Write the numbers 4,12 in a row
- Divide them by their common prime factors, if there is one
- Carry forward the numbers that are left undivided by the previously chosen factor
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM(4,12) = 12
Common Mistakes and how to avoid them while finding the LCM of 4 and 12
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 4 and 12. Try to avoid them.
Mistake 1
Listing incorrect multiples
If the LCM of given numbers is 12, double-check that the number appears on the list of both 4 and 12.
Mistake 2
Prime factorization errors
Check if the numbers are prime factored correctly. For example, we may accidentally write 12 = 2×2×2 instead of 12= 2×2×3
Mistake 3
Thinking product is the LCM
One may think the product of the numbers is the LCM of the numbers. This is only true in case of co-prime numbers
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LCM of 4 and 12 Examples
Problem 1
The LCM of 4 and 12 is 12. What is the percentage increase from the smaller number to the LCM?
Smaller number = 4, LCM = 12
Percentage increase = 12−44×100=200%
Explanation
The LCM is 200% larger than the smaller number (4).
Problem 2
Employee A and employee B work different shifts. A works every 4 days, and B every 12 days. If they both work on the same day today, when will they next work together?
The LCM of 4 and 12 is 12.
Explanation
Both employees will work together again in 12 days. The LCM of 4 and 12 is 12, which is the smallest time interval between the digits.
Problem 3
Use the relationship LCM(a,b)=a×b/GCF(a,b) to find the LCM of 4 and 12.
GCD(4,12)=4
LCM(4,12)=4×12/4=12
Explanation
The formula LCM(a,b)=a×b/GCF(a,b),​ gives a quick way to calculate the LCM by using the greatest common divisor.
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FAQs on LCM of 4 and 12
1.What is the HCF of 4 and 12?
2.What are the common factors of 4 and 12 ?
3.What is the LCM of 8,4 and 12 ?
4.How many multiples of 4 are in 12?
5.Is 0 a multiple of 4?
6.How can children in United States use numbers in everyday life to understand LCM of 4 and 12?
7.What are some fun ways kids in United States can practice LCM of 4 and 12 with numbers?
8.What role do numbers and LCM of 4 and 12 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 4 and 12 skills?
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Important glossaries for the LCM of 4 and 12
- Multiple — product of a number and a natural integer
- Prime factor — number one gets after prime factorization any given number
- Prime factorization — the process of breaking the number into its prime factors.
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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.
