LCM of 12 and 15
2026-02-21 20:37 Diff
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Last updated on August 5, 2025

LCM is a common multiple, the smallest value between the numbers 12 and 15. 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 12 and 15?

LCM of 12 and 15 Using Listing the Multiples

Step1; Write down the multiples of the numbers. Don’t stop too early.


12 = 12,24,48,60 …


15 = 15,60,45,60,75,…


 Step 2: Find the smallest number common between the written multiples of 12 and 15 


      — The smallest common multiple is 60.


Thus, LCM(12,15) = 60
 

LCM of 12 and 15 Using Prime Factorization

Step 1— factorize the numbers into its prime factors 


12 =2×2×3


15 =5×3


Step 2— find the highest powers of the factors of 12 and 15


Step 3— Multiply the highest powers 


LCM(12,15) = 60
 

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LCM of 12 and 15 Using Division Method

  • Write the numbers 12, 15 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(12,15) = 60 
     

Common Mistakes and how to avoid them while finding the LCM of 12 and 15

Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 12 and 15. Try to avoid them. 
 

Problem 1

The GCF of two numbers is 3, and one of the numbers is 12. If the LCM of the two numbers is 60, find the missing number.

Okay, lets begin

Using the formula LCM(a,b)×GCF(a,b)=a×b:


60×3=12×Missing Number


180=12×Missing Number


Missing Number=180/12=15
 

Explanation

The missing number is 15.
 

Well explained 👍

Problem 2

Find the ratio of the GCF to the LCM of 12 and 15.

Okay, lets begin

GCF of 12 and 15 = 3 (from Problem 3)


LCM of 12 and 15 = 60 (from Problem 1)


Ratio = GCF/LCM=3/60=1/20
 

Explanation

The ratio of the GCD to the LCM is 1:20.
 

Well explained 👍

Problem 3

Add the fractions 5/12 and 7/15 by finding the LCM of the denominators.

Okay, lets begin

Answer: 5/12+7/15=53/60
 

Explanation

LCM of 12 and 15 = 60


Convert to common denominator:


5/12=5×5/60=25/60


7/15=7×4/60=28/60​


Sum: 25/60+28/60=53/60
 

Well explained 👍

FAQs on LCM of 12 and 15

1.What is the LCM of 5,15 and 20?

60 is the smallest number that appears commonly on the lists of the numbers 5,15 and 20. 
LCM (5,15,20) = 60 
 

2.What is the HCF of 5 and 20?

HCF of 5 and 20 can be found by listing the factors of the numbers → finding the largest common factor from the list of numbers. 


Factors of 5 = 1,5 


Factors of 20 = 1,2,4,5,10,20 


HCF (5,20) = 5 

3. Is 20 a multiple of 5?

Yes, 5 is a multiple of 20. When divided, no reminders are left behind. 


20/5 = 4
 

4. Is 0 a multiple of 5?

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

5.What is the LCM of 17 and 11?

187 is the smallest number that appears commonly on the lists of the numbers 11 and 17.


LCM (11,17) =187 
 

Important glossaries on the LCM of 12 and 15

  • 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.