LCM of 12 and 30
2026-02-28 12:44 Diff
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Last updated on August 5, 2025

LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events. The Least common multiple (LCM) is the smallest number that is divisible by the numbers 12 and 30.

What is the LCM of 12 and 30?

How to find the LCM of 12 and 30 ?

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

LCM of 12 and 30 using the Listing multiples method

The LCM of 12 and 30 can be found using the following steps;


Step 1: Write down the multiples of each number: 


Multiples of 12 = 12,24,36,48,60…


Multiples of 30 = 30,60,…


Step 2: Ascertain the smallest multiple from the listed multiples of 12 and 30. The least common multiple of the numbers 12 and 30 is 60. 
 

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LCM of 12 and 30 using the Prime Factorization

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.


Step 1: Find the prime factors of the numbers:


Prime factorization of 12  = 2×2×3


Prime factorization of 30  = 2×5×3

Step 2: Multiply the highest power of each factor ascertained to get the LCM: 


LCM (12,30) = 60

LCM of 12 and 30 using the Division Method

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

Step 1: Write down the numbers in a row;

Step 2:A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.

Step 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.

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


LCM (12,30) = 60
 

Common Mistakes and how to avoid them while finding the LCM of 12 and 30

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 12 and 30, make a note while practicing.
 

Problem 1

The LCM of a and b is 36 and the sum of a and b is 21. Find a and b.

Okay, lets begin

LCM(a, b) = 36 


a+b= 21


We know that, LCM(a,b)×HCF(a,b) =a×b 


Let us assume that the numbers a and b are 8 and 10, 


8+10 = 18, it is not equal to the sum given


Let us assume that the numbers a and b are 12 and 30,


30+12= 42, which is equal to the sum given


Product of 12 and 30; 


30 ×12= 360


LCM(a,b)×HCF(a,b) =a×b 


LCM(30,12)×HCF(30,12) =30×12 


LCM of 30,12; 


Prime factorization of 12  = 2×2×3


Prime factorization of 30 =  5×2×3


LCM(30,12) = 60


HCF of 30,12; 


Factors of 30 = 1,2,3,5,6,10,15,30 


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


HCF(30,12) = 6


60×6 =30×12 


360 =360 

Explanation

We, by assuming that a and b are 12 and 30 respectively and verifying the same against the formula figures that the assumption is right and a=12,b=30. 
 

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Problem 2

The LCM of 9 and ‘b’ is 36. 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(9,b) = 36 


and, a = 9


Applying LCM(a, b) = a×b/HCF(a, b) 


36 = 9×b/HCF(9, b) 


36 = 9×b/3 


b= 36×3/9= 12


b= 12 
 

Explanation

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

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Problem 3

Two vans arrive at a store every 12 and 30 minutes, respectively, for a delivery. If they both arrive at the station at 8:00 AM, when will they arrive together again?

Okay, lets begin

 The LCM of 12 and 30 is 60. 

Explanation

The vans will arrive at the station together again in 60 minutes, which will be at 9:00 AM. 60 is the LCM that expresses the smallest common time interval between 12 and 30. 
 

Well explained 👍

FAQ’s on LCM of 12 and 30

1.Is 6 a factor of 0?

Yes, 6 is a factor of 0. In fact, all non-zero numbers are factors of 0. 
 

2.What is the HCF of 12 and 30?

Factors of 12–1,2,3,4,6,12


Factors of 30–1,2,3,5,6,10,15,30


HCF(12,30) = 6
 

3.What is the LCM of 10,12 and 30?

Prime factorization of 10 =  2×5


Prime factorization of 12  = 2×2×3


Prime factorization of 30  = 2×5×3


LCM (10,12,30) = 60
 

4.What is the LCM of 12 and 32?

Prime factorization of 12  = 2×2×3


Prime factorization of 32  = 2×2×2×2×2


LCM (12,32) = 96
 

5.What is the LCM of 12,24 and 30?

Prime factorization of 12  = 2×2×3


Prime factorization of 24  = 2×2×3×2


Prime factorization of 30  = 2×5×3


LCM (12,24,30) = 120 
 

Important glossaries for LCM of 12 and 30

  • 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. 
  • 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.