LCM of 8 and 12
2026-02-28 17:44 Diff
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Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 and 12. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 8 and 12?

How to find the LCM of 8 and 12 ?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 8 and 12 using the Listing multiples method

To ascertain the LCM, list the multiples of the integers until a common multiple is found. 


Steps:


1. Writedown the multiples of each number: 


Multiples of 8 = 8,16,24,32…
Multiples of 12 = 12,24,36… 


2. Ascertain the smallest multiple from the listed multiples of 8 and 12. 


The LCM (Least common multiple) of 8 and 12 is 24. i.e., 24 is divisible by 8 and 12 with no reminder.
 

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LCM of 8 and 12 using the Prime Factorization

This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.


Steps: 


1. Find the prime factors of the numbers:

  • Prime factorization of 8 = 2×2×2
  • Prime factorization of 12 = 2×2×3


2.  Take the highest power of each prime factor:


= 2,2,2,3


3. Multiply the ascertained factors to get the LCM: 


LCM (8,12) = 2×2×2×3 = 24

LCM of 8 and 12 using the Division Method

The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

Steps:

1. Write down the numbers in a row;

2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. 

3. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

4. The LCM of the numbers is the product of the prime numbers in the first column, i.e., 

2×2×2×3= 24 

LCM (8,12) = 24

Common Mistakes and How to Avoid Them in LCM of 8 and 12

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8 and 12, make a note while practicing.

Problem 1

The LCM of 8 and ‘b’ is 24. Ascertain b.

Okay, lets begin

The LCM of a and b can be found using -  LCM(a, b) = a×b/HCF(a, b) 


We know the LCM(8,b) = 24 
and, a = 8


Applying LCM(a, b) = a×b/HCF(a, b) 

24 = 8×b/HCF(8, b) 


b= 24×HCF(8, b)/8 


24×4/8 = 12


b= 12

Explanation

The other number, b is 12. We apply the formula as aforementioned to ascertain the missing number. 

Well explained 👍

Problem 2

Verify the relationship between the HCF and the LCM of 8 and 12 using LCM(a,b)×HCF(a,b) =a×b

Okay, lets begin

The LCM of 8 and 12;


Prime factorization of 8 = 2×2×2


Prime factorization of 12 = 2×2×3  


LCM(8,12) = 24 


HCF of 8 and 12; 


Factors of 8 = 1,2,4,8


Factors of 12 = 1,2,3,4,6,12 


HCF(8,12) = 4 


Verify the ascertained LCM and HCF by applying them in the formula;


LCM(a,b)×HCF(a,b) =a×b 


LCM(8,12)×HCF(8,12) =8×12 


24×4 =96 

Explanation

Both sides are equal, hence, the relationship between the HCF and LCM of 8 and 12 is verified.

Well explained 👍

Problem 3

The LCM of a and b is 24 and their HCF is 4, what is the product of a and b?

Okay, lets begin

Using the formula; 


LCM(a,b)×HCF(a,b) =a×b 


Given; LCM = 24 


HCF = 4


24×4 =a×b = 96

Explanation

The product of a and b can be ascertained using the mentioned formula; LCM(a,b)×HCF(a,b) =a×b. Using the same, we derived that the product of a and b is 96.

Well explained 👍

Problem 4

Trains A and B arrive every 8 minutes and 12 minutes at the station at the same time. In how long will they arrive together again?

Okay, lets begin

The LCM of 8 and 12 =24. 

Explanation

The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 24 minutes.

Well explained 👍

FAQ’s on LCM of 8 and 12

1.Is multiplying 8 and 12 the correct way to find the LCM?

No, multiplying gives you the product of the numbers, in this case,96. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

2.Why is the LCM of 8 and 12, not 12?

12 is not a multiple of 8, so it can’t be the LCM. LCM has to be the smallest number that both 8 and 12 divide into, which is 24.

3.What is the LCM formula using the HCF?

  • The method below elaborates on how to derive the LCM using HCF (Highest common factor). An example is also attached to check the validity.  

LCM (a, b)= a×b/HCF(a, b)

For the given numbers 8 and 12, HCF(8,12)=4 

So, LCM(8,12)=8×12/4 = 24

By following the above, we can state that the LCM of numbers 8 and 12 can be found using their HCF, which is 4.

4.Is the LCM of 8 and 12 always a multiple of their HCF?

The LCM is always a multiple of HCF. For the numbers 8 and 12, the HCF is 2, and 24 (the LCM) is a multiple of 2.

Important glossaries for LCM of 8 and 12

  • Multiple: A number and any integer multiplied. 
  • Prime Factor: A natural number (other than 1) that has factors that are one and itself.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 
  • Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 
  • Relatively Prime Numbers: Numbers that have no common factors other than 1.
  • Fraction: A representation of a part of a whole.

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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.