LCM of 5 and 12
2026-02-28 17:52 Diff
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Last updated on August 5, 2025

LCM is a common multiple, the smallest value between the numbers 5 and 12. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.

LCM of 5 and 12 using the Listing Multiples Method

Step 1: Write down the multiples of the numbers. Don’t stop too early.


  — Multiples of 5 = 5,10,15,20,26,30,35,40,45,50,55,60,…


  — Multiples of 12 = 12, 24, 36, 48, 60, 52, 60, …


 Step 2: Find the smallest number common between the written multiples of 3 and 8


      — The smallest common multiple is 60


Thus, LCM(5,12) = 60

LCM of 5 and 12 using the Prime Factorization Method

 Step 1:— factorize the numbers into its prime factors 


5 = 5×1


12 = 2×2×3


 Step 2:— find the highest powers of the factors of 5 and 12


 Step 3:— Multiply the highest powers 


LCM(5,12) = 60

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LCM of 5 and 12 using the Division Method

  • Write the numbers 5,12 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(5,12) = 60

Common Mistakes and how to avoid them while finding the LCM of 5 and 12

Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 5 and 12. Try to avoid them. 
 

Problem 1

A movie theater alternates between a crime film and a children’s film. The crime film is shown every 5 days and the children’s film is shown every 12 days. In how many days will they both be screened together?

Okay, lets begin

The LCM of 5 and 12 is 60.  
 

Explanation

Both films will be shown on the same day again in 60 days. The LCM of 5 and 12 is 60, which is the smallest common time interval between the digits. 
 

Well explained 👍

Problem 2

How many times does the LCM of 5 and 12 occur between 1 and 300?

Okay, lets begin

LCM of 5 and 12 is 60.


Divide 300 by 60 to find how many times it occurs: 300/60=5
 

Explanation

So, the LCM of 5 and 12 occurs 5 times between 1 and 300
 

Well explained 👍

Problem 3

Verify the LCM of 5 and 12 using the formula LCM(a,b)=a×bGCD(a,b)

Okay, lets begin

a=5, b=12


GCD of 5 and 12 is 1 (because 5 and 12 share no common factors).


Using the formula: 


LCM(5,12)=5×12/1=60
 

Explanation

 Therefore, the LCM is 60, confirming the result.
 

Well explained 👍

FAQs on LCM of 5 and 12

1.What is the LCM of 5,12 and 20?

LCM(5,12,20) = 60.


60 is the smallest number that appears commonly on the lists of the numbers 5,12,20.
 

2.What are the common factors of 5 and 12 ?

Factors of 5–1,5 


Factors of 12–1,2,3,4,6,12


There are no common factors between the digits but 1, hence, GCF =1. 
 

3.What are the multiples of 5 and 12?

— Multiples of 5 = 5,10,15,20,25,30,35,40,45,50,55,60…


— Multiples of 12 =12,24,36,48,60,72,84,96,108,120… 


5 and 12 share the common multiple 60 which is also the LCM of the numbers. 
 

4.What is the LCM of 5,4 and 12?

60 is the smallest number that appears commonly on the lists of the numbers 5,4 and 12


LCM(5,4,12) = 60
 

5.What is divisible by both 5 and 12?

The LCM of the numbers 5 and 12 is 60, therefore all multiples of 60 are divisible by both 5 and 12. 
 

Important glossaries for the LCM of 5 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.