LCM of 4 and 12
2026-02-28 17:48 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-4-and-12

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Last updated on August 5, 2025

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?

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

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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. 
 

Problem 1

The LCM of 4 and 12 is 12. What is the percentage increase from the smaller number to the LCM?

Okay, lets begin

Smaller number = 4, LCM = 12


Percentage increase = 12−44×100=200%
 

Explanation

The LCM is 200% larger than the smaller number (4).
 

Well explained 👍

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?

Okay, lets begin

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. 

Well explained 👍

Problem 3

Use the relationship LCM(a,b)=a×b/GCF(a,b) to find the LCM of 4 and 12.

Okay, lets begin

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.
 

Well explained 👍

FAQs on LCM of 4 and 12

1.What is the HCF of 4 and 12?

HCF of 4 and 12 can be found by listing the factors of the numbers → finding the largest common factor from the list of numbers.


Factors of 4: 1,2,4


Factors of 12: 1,2,3,4,6,12


HCF (4,12)= 4 
 

2.What are the common factors of 4 and 12 ?

Factors of 4: 1,2,4


Factors of 12: 1,2,3,4,6,12


Common factors of the numbers: 1,2,4
 

3.What is the LCM of 8,4 and 12 ?

24 is the smallest number that appears commonly on the lists of the numbers 8,4 and 12. 


LCM (4,8,12) = 24
 

4.How many multiples of 4 are in 12?

The product of a number and a natural integer is called a multiple. The multiples of 4 up to 12 are just 2, 4 and 8. 

5.Is 0 a multiple of 4?

The product of a number and a natural integer is a multiple. 


Yes, any non-zero number is a multiple of 0. 
 

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.