LCM of 7 and 12
2026-02-28 11:21 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-7-and-12

476 Learners

Last updated on August 5, 2025

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.

What is the LCM of 7 and 12?

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;

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

Explore Our Programs

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

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

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.

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?

Okay, lets 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.

Well explained 👍

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?

Okay, lets 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.

Well explained 👍

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?

Okay, lets 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.

Well explained 👍

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?

Okay, lets 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.

Well explained 👍

FAQs on LCM of 7 and 12

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

Multiplying gives you the product of the numbers. LCM, however, is the smallest common multiple that can be ascertained following the methods mentioned above.

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

You can find the LCM For exponential equations with different bases by following the below example,

  • Find the LCM of 74×122 and 73×123
  • Factorize the terms and find the highest power 

Highest power of 7 =  74

Highest power of 12=  123

LCM =  74 ×123

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

  • The relationship between GCD and LCM is expressed by the formula:  

     LCM(a,b)×HCF(a,b)=a×b

Verifying this, 

LCM(7,12)×HCF(7,12)= 84×1

—> 84=84

This formula shows how the GCD/HCF and LCM complement each other.

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

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

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.