BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon172 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

LCM of 7 and 12

Professor Greenline Explaining Math Concepts

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 7 and 12. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

LCM of 7 and 12 for Indian Students
Professor Greenline from BrightChamps

What is the LCM of 7 and 12?

The LCM of 7 and 12 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 7 and 12?

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 7 and 12 using the Listing Multiples Method

The LCM of 7 and 12 can be calculated using the following steps:

Steps:

  1. Write down the multiples of each number

  — Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …

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

  1. Ascertain the smallest multiple from the listed multiples:

  — The smallest common multiple is 84.

Thus, LCM(7, 12) = 84

Professor Greenline from BrightChamps

LCM of 7 and 12 using the Prime Factorization Method

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

Steps:

  1.  Prime factorization of 7 = 7 (since 7 is prime)
  2. Prime factorization of 12 = 2 × 2 × 3 
  3. Take the highest powers of each prime factor and multiply the highest powers to get the LCM:

—  LCM(7, 12) = 2² × 3 × 7 = 84

Professor Greenline from BrightChamps

LCM of 7 and 12 using the Division Method

This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.

 

Steps:

— Write the numbers. Divide by common prime factors and multiply the divisors. 

  — 2 × 2 × 3 × 7 = 84

Thus, LCM(7, 12) = 84

Max Pointing Out Common Math Mistakes

Common Mistakes and how to avoid them while finding the LCM of 7 and 12

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 and 12, 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 7 and 12

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

This can be avoided by always double-checking the multiples of the numbers 7 and 12 and by not stopping too early. To elaborate, listing 7,14 as multiples of 7 and 12,24 as multiples of 12 and assuming 24 is the LCM.

Max from BrightChamps Saying "Hey"

LCM of 7 and 12 Examples

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

Problem 1

A movie theater alternates between a crime film and a children’s film. The crime film is shown every 7 days and the children’s film is shown every 12 days. In how many days will they both be screened together?

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

The LCM of 7 and 12 is 84. 

Explanation

Both films will be shown on the same day again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.

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

Problem 2

An HP Printer prints a batch every 7 minutes and a Canon printer prints a batch every 12 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?

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

The LCM of 7 and 12 is 84.

Explanation

Both machines will print a batch together at 11:24AM. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.

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

Problem 3

The sprinkler watering system waters every 7 days and the drip watering system waters every 12 days. On which day do they have to be turned on together?

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

The LCM of 7 and 12 is 84.

Explanation

Both the watering systems have to be turned on together in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.

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

Problem 4

An assembly is held every 7 days and a debate competition every 12 days. If both the events occur today, in how many days will they occur together again?

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

The LCM of 7 and 12 is 84.

Explanation

The events will occur together again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.

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

FAQs on LCM of 7 and 12

1.Why is the LCM of 7 and 12 not simply their product (7 × 12 = 84) ?

Math FAQ Answers Dropdown Arrow

2.How do you find the LCM with different bases in an exponential equation ?

Math FAQ Answers Dropdown Arrow

3.What is the relationship between the Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) and LCM of 7 and 12?

Math FAQ Answers Dropdown Arrow

4.What are the factors of 7 and 12?

Math FAQ Answers Dropdown Arrow

5.Find the LCM of 7 and 12 using the continuous division method.

Math FAQ Answers Dropdown Arrow

6.How can children in India use numbers in everyday life to understand LCM of 7 and 12?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

8.What role do numbers and LCM of 7 and 12 play in helping children in India develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in India create number-rich environments to improve LCM of 7 and 12 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important glossaries for the LCM of 7 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 or a whole
Professor Greenline from BrightChamps

About BrightChamps in India

At BrightChamps, we understand numbers are much more than just digits—they open doors to endless possibilities! We strive to help children all across India master key math skills, focusing today on the LCM of 7 and 12 with a special emphasis on understanding the LCM—in a way that’s lively, enjoyable, and easy to understand. Whether your child is calculating how fast a train passes by, keeping scores during a cricket match, or managing pocket money to buy new gadgets, mastering numbers boosts their confidence for everyday situations. Our interactive lessons make learning simple and fun. Since children in India have varied learning styles, we customize our teaching to fit each child. From the bustling markets of Mumbai to the vibrant streets of Delhi, BrightChamps brings math to life, making it relatable and exciting all across India. Let’s make the LCM an enjoyable part of every child’s math learning!
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