LCM of 3, 4 and 7
2026-02-28 19:18 Diff
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Last updated on August 5, 2025

LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, as distributing any items among others. In this topic, we will learn more about LCM of 3, 4, and 7.

What is the LCM of 3, 4, and 7

The common multiple of 3, 4, and 7 is 84.  Here, we will learn about the LCM of 3 numbers. Children learn about LCM at younger ages. Here, we will discuss the methods used for finding out LCM.
 

How to find the LCM of 3, 4, and 7?

Out of many methods, prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows - 

  1. Listing Of Multiples
  2. Prime Factorization
  3. Division Method
     

LCM of 3, 4, and 7 Using Listing the Multiples

Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 3 numbers is noted - 

  • Multiples of 3: 3, 6, 9, 12, 15, 18, ……, 84
  • Multiples of 4: 4, 8, 12, 16, 20, ........., 84
  • Multiples of 7: 7, 14, 21, 28, 35, ......., 84


Then we can see that out of 3, 4, and 7, 84 is the smallest common number that is present in them. So we see that 84 is the LCM of 3, 4, and 7.
 

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LCM of 3, 4, and 7 Using Prime Factorization

The product of the highest power of prime factors of 3, 4, and 7 is the LCM of these numbers. So let us look at it step by step to understand it better.


Breaking the given numbers into their prime factors.


Prime factorization of 3 = 31 
Prime factorization of 4 = 22
Prime factorization of 7 = 71


Multiplying the highest power of prime factors: 22 × 31 × 71 → 4 × 3 × 7 = 84


LCM of 3, 4, and 7 is 84.
 

LCM of 3, 4, and 7 Using Division Method

In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.


Step 1: Arrange the number in a sequence, divisors, and the numbers are on the left and right sides respectively.


Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 3, 4, and 7 by 2. The result is 3, 2, and 7. 


Step 3: As 2 is divisible by 2, again the divisor is 2. Dividing 3, 2, and 7 by 2. Now the result is 3, 1, and 7.


Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.

The divisors are 2, 2, 3, 7. LCM of 3, 4, and 7 is the product of divisors.


Hence, the LCM of (3, 4, and 7) =2 × 2 × 3 × 7 =84

Common Mistakes and How to Avoid Them in LCM of 3, 4, and 7.

There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.
 

Problem 1

Three maintenance routines for machines are scheduled every 3, 4, and 7 weeks, respectively. If they are all done this week, after how many weeks will all maintenance routines coincide again?

Okay, lets begin

List the multiples of 3:3, 6, 9, 12, 15, 18, ……84
List the multiples of 4:4, 8, 12, 16, 20,.........84
List the multiples of 7:7, 14, 21, 28, 35,......84


So, we get the smallest common multiple in both lists as 84


So the LCM of 3,4 and 7 is 84 (which is 84 weeks) 
 

Explanation

So, all maintenance routines will coincide again in 84 weeks. 

Well explained 👍

Problem 2

A teacher wants to schedule a review session for three groups of students. Group A has a session, every 3 days, Group B every 4 days, and Group C every 7 days. If all groups meet today, when will all groups meet on the same day again?

Okay, lets begin

Step 1: 3, 4, and 7 → Write the prime factors 


Prime factor of 3:31
Prime factor of 4:2  × 2
Prime factor of 7:71


Prime factorization of LCM of 3,4 and 7 in exponential form is : 


3=31
4=22
7 = 71


Step 2: Find the highest power and multiply together.


After multiplying, we get 22  × 31  × 7 1  =4 × 3 × 7 =84(84 days) 

Explanation

So, here, we get the answer 84. This means all groups will meet on the same day again in 84 days. 
 

Well explained 👍

Problem 3

To calculate the LCM of 3, 4, and 7 by using the division method.

Okay, lets begin

 by division method, 


Step 1: Write the numbers 3, 4, and 7 


Step 2: Then divide by the smallest common prime factor, and continue dividing by other prime numbers till the remainder is 1.

Now multiply by the divisor, and we get 2 × 2 × 3 × 7 =84


 The LCM of 3, 4, and 7 is 84.
 

Explanation

The division method includes dividing the numbers by their prime factors and multiplying the divisor to get the LCM. 
 

Well explained 👍

FAQ on LCM of 3, 5 and 7

1.What are the multiples of 2, 5, and 6?

The first few multiples of 2, 5, and 6 are 2, 4, 6, 8, 10; 5, 10, 15, 20, 25; and 6, 12, 18, 24, 30 respectively. 
 

2.What is the LCM of 2, 6, and 6?

 The smallest multiple divisible by 2 and 6 is 6. So the LCM of 2, 6, and 6 is 6
 

3.What is the LCM of 2, 5, and 6?

The Least common multiple of 2, 5, and 6 is 30.
 

4.What is the LCM of 5 and 7?

 The LCM of 5 and 7 is 35. To find the LCM, write the multiple of 5 and 7, then choose the smallest multiple that can be exactly divisible by 5 and 7. 
 

5.What is the LCM of 9 and 12?

Important Glossaries of LCM 3, 5, and 7

  • Factor: A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.
  • Prime Factorization: When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.
  • Greatest Common Factor (GCF): GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.
  • Division Method: In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1. 

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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.