BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon175 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

LCM of 12 and 30

Professor Greenline Explaining Math Concepts

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.

LCM of 12 and 30 for Filipino Students
Professor Greenline from BrightChamps

What is the LCM of 12 and 30?

The LCM of 12 and 30 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators. 
 

Professor Greenline from BrightChamps

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; 
 

Professor Greenline from BrightChamps

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. 
 

Professor Greenline from BrightChamps

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

Professor Greenline from BrightChamps

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
 

Max Pointing Out Common Math Mistakes

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.
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

 Listing incorrect/overlooking multiples for the given numbers 12 and 30. 
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

This can be avoided by always double-checking the multiples of the numbers 12 and 30 and by not stopping too early. To elaborate, listing 12,24 as multiples of 12 and 30,60,90 as multiples of 30 and assuming 24 is the LCM. 
 

Max from BrightChamps Saying "Hey"

LCM of 12 and 30, Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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. 
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

The LCM of 9 and ‘b’ is 36. Ascertain b.

Ray, the Boy Character from BrightChamps Saying "Let’s 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. 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s 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. 
 

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ’s on LCM of 12 and 30

1.Is 6 a factor of 0?

Math FAQ Answers Dropdown Arrow

2.What is the HCF of 12 and 30?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

4.What is the LCM of 12 and 32?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

6.How can children in Philippines use numbers in everyday life to understand LCM of 12 and 30?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in Philippines can practice LCM of 12 and 30 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and LCM of 12 and 30 play in helping children in Philippines develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in Philippines create number-rich environments to improve LCM of 12 and 30 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Philippines

At BrightChamps, we know numbers are more than just digits—they open up a world of possibilities! We’re here to help kids across the Philippines build key math skills, focusing on the LCM of 12 and 30 with special attention to understanding the LCM—in a lively, fun, and easy way. Whether your child is working out the speed of a roller coaster at Enchanted Kingdom, keeping track of basketball scores, or managing allowance to buy gadgets, mastering numbers boosts their confidence for everyday life. Our interactive lessons make learning both simple and fun. Since children in the Philippines learn in many different ways, we adapt our approach to fit each learner. From Manila’s bustling streets to the beautiful islands of Palawan, BrightChamps makes math exciting and relatable. Let’s make learning the LCM enjoyable for all!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom