LCM of 6 and 7
2026-02-28 09:55 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-6-and-7

400 Learners

Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 7. 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 6 and 7?

How to find the LCM of 6 and 7?

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

LCM of 6 and 7 using the Listing Multiples Method

The LCM of 6 and 7 can be found using the following steps:


Step 1: Write down the multiples of each number


Multiples of 6 = 6,12,…42,…


Multiples of 7 = 7,14,…42,…


Step 2: Ascertain the smallest common multiple from the listed multiples


  The smallest common multiple is 42


Thus, LCM(6, 7) = 42.
 

Explore Our Programs

LCM of 6 and 7 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.


Step 1: Find the prime factors of the numbers:


Prime factorization of 6 = 2×3


 Prime factorization of 7 = 7

Step 2: Take the highest powers of each prime factor:


Highest power of prime factors= 2,3


Highest power of prime factor = 7


Step 3: Multiply the highest powers to get the LCM:


LCM(6, 7) =   2 ×3 × 7= 42

LCM of 6 and 7 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

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. 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 3:   2× 3 × 7= 42

Common Mistakes and how to avoid them in LCM of 6 and 7

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 7, make a note while practicing.
 

Problem 1

What is the least perfect square divisible by 6 and 7?

Okay, lets begin

Follow the below steps to find the least perfect square that is divisible by the numbers 6 and 7; 


Step 1 — Prime factorize the numbers 


6 = 2×3


7 = 7


Step 2  — Find the LCM 


LCM(6,7) = 2×3×7 = 42


Step 3 — Adjust the numbers for a perfect square, to do so to make all the exponents even. Multiply the numbers

21×31×71, which will give;


 42×42 = 22×32×72 = 1764    
 

Explanation

The least perfect square divisible by both the numbers is 1764.
 

Well explained 👍

Problem 2

Elaborate on the relationship between HCF and LCM of 6 and 7.

Okay, lets begin

The relationship between HCF and LCM can be verified using this formula; HCF(a,b)×LCM(a,b) = a×b


HCF of 6,7 = 1 (6,7 are relatively prime numbers) 


LCM of 6,7 = 42


Now apply the formula, 


HCF(a,b)×LCM(a,b) = a×b


HCF(6,7)×LCM(6,7) = 6×7


1×42 = 42 


42 = 42

Explanation

 The above explains the relationship between the HCF and the LCM of 6 and 7. The given formula works to verify the relationship between the HCF and LCM for any given pair of numbers. 

Well explained 👍

Problem 3

Find the LCM of 6 and 7 using a Venn diagram.

Okay, lets begin

List the factors of the numbers;


— 6 —> 2,3


— 7 —> 7 

Explanation

 The numbers have no common factors, therefore the numbers are listed in their own circles and are multiplied. The LCM (6,7) = 42. 
 

Well explained 👍

Problem 4

Elevator F stops on the first floor every 6 minutes and elevator Y stops every 7 minutes. If they both stop on the first floor now, when will they both stop at the same time next?

Okay, lets begin

The LCM of 6 and 7 is 42. 
 

Explanation

The smallest common multiple between the numbers 6 and 7 is 42. So, we can say that in 42 minutes, elevators F and Y will stop at the same time on the first floor.
 

Well explained 👍

FAQs on LCM of 6 and 7

1.What do 6 and 7 have in common?

6 and 7 share distinct prime factor combinations, the only common factor they share is 1. 


Factors of 6: 1,2,3,6


Factors of 7: 1,7 
 

2.Is 42 a multiple of 6 and 7?

Yes, 42 is a multiple of both 6 and 7. 6 times 7 and vice versa is 42. 
 

3.Is 69 a multiple of 6?

No, 69 is not a multiple of 6. When divided, it leaves behind a remainder of 3.

4.Is 42 the LCM of 6 and 7?

Yes, the LCM of 6 and 7 is 42. The numbers have no common factors, and the least common multiple they share is 42. 
 

5.What is the LCM of 6,7 and 9?

Step 1: Find the prime factors of the numbers:


Prime factorization of 6 = 2×3


Prime factorization of 7 = 7


Prime factorization of 9 = 3×3


Step 2: Take the highest powers of each prime factor:


Highest power of 6 = 21,31


Highest power of 7 = 7


Highest power of 9 = 32


Step 3: Multiply the highest powers to get the LCM:


LCM(6, 7,9) =   2 ×32× 7= 126
 

Important glossaries for the LCM of 6 and 7

  • Prime Factor: A natural number (other than 1) whose factors are only one and itself.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 
  • Relatively Prime Numbers: Numbers that have no common factors other than 1.
     

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

▶