LCM of 6, 72 and 120
2026-02-28 17:28 Diff
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Last updated on August 5, 2025

Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 6, 7, and 120. By learning the following tricks, you can learn the LCM of 6, 7, and 120 easily.

What is the LCM of 6, 72 and 120?

The LCM of 6, 7, and 120 is 360. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.

How to find the LCM of 6,72, and120?

We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:


Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method


Now let us delve further into these three methods and how it benefits us. 
 

LCM of 6, 72, and 120 Using Listing the Multiples

In this method, we will list all the multiples of 6, 72, and 120. Then we will try to find a multiple that is present in both numbers.


For example, 


Multiples of 6: 6, 12, 18, 24, 30,…360


Multiples of 72:  72, 144, 216, 288, 360


Multiples of 120:  120, 240, 360, 480, 600

The LCM of 6, 7, and 120 360. 360 is the smallest number which can be divisible by both 6, 72, and 120.
 

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LCM of 6, 72 and 120 Using Prime Factorization

To find the LCM of 6, 72, and 120 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM.


Prime factors of 6 are:  2×3


Prime factors of 72 are: 2×2×2×3×3


Prime factors of 120 are: 2×2×2×3×5


Multiply the highest power of both the factors : 23 x 32 x 51 = 360


Therefore, the LCM of 6, 72, 120 is 360
 

LCM OF 6,72, and 120 Using Division Method

To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.

For finding the LCM of 6, 7, and 120 we will use the following method.

By multiplying the prime divisors from the table, we will get the LCM of 6, 7, and 120.

2 x 2 x 2 x 3 x 3 x 5 = 360

The LCM of 6, 7, and 120  = 360

Common Mistakes and How to Avoid Them in LCM of 6,72 and 120

Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
 

Problem 1

Find x LCM (6,72,x) = 360?

Okay, lets begin

The LCM of 6,72 = 360


The LCM of 6,72 and x should be the number that is divisible by all three numbers.


The LCM remains at 120,


Common factor of 120 = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,and 120.
 

Explanation

The desirable values for x will be any one of the listed factors. The LCM with all the numbers above remains at 120.
 

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Problem 2

There are three movies showing in the local cinemas. The first movie plays every 6 hours, the second every 72, and the third every 120 hours. Today all three movies are showing at the same time, so after how many hours will all three movies show at the same time?

Okay, lets begin

Numbers of hours the first movie is shown = 6
Numbers of hours the second movie is shown = 72 
Numbers of hours the third movie is shown = 120

The numbers it will take for all three movies to show at once  = LCM of 6, 72, and 120 = 360 hours
 

Explanation

Hence, every 360 hours, all the movies will be played at once in the local cinemas.
 

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Problem 3

Find the smallest number that is exactly divisible by 6,72, and 120.

Okay, lets begin

Here, The value of LCM (6,72,120) will be the smallest number that is correctly divisible by 6,72,120.
Then multiples of numbers 6,72,120 


Multiple of 6 = 6,12,18,24,30,36,42,48,54,60……336,342,348,354,360…


Multiple of 72 = 72,144,216,288,360,432,504…..


Multiple 120  = 120,240,360,480,600,720,840….


Accordingly, the LCM OF 6,72 and 120 is 360.
 

Explanation

Here is the smallest number that is exactly divisible by 6,72, and 120 is also 360.

Well explained 👍

Problem 4

A bus travels to the mall every 6 hours, another bus travels to the mall every 72 hours. A third bus travels to the same mall every 120 hours. How many hours will it take for all three buses to meet at the same time?

Okay, lets begin

Numbers of hours the first bus arrives in = 6


Numbers of hours the second bus arrives in = 72


Numbers of hours the third bus arrives in = 120
 

Explanation

The number of hours it will take for all three buses to arrive at the same time = LCM of 6, 7, and 120 = 360 hours

Hence, every 360 hours, all the three buses will arrive at the same time.
 

Well explained 👍

Problem 5

There are three lights blinking at different intervals. The first light blinks every 6 seconds, the second light blinks every 72 seconds and the third blinks every 120 seconds. After how many seconds will they blink together again?

Okay, lets begin

The interval of the first light  = 6 seconds


The interval of the second light  = 72 seconds


The interval of the third light  = 120 seconds

Explanation

 The amount of time it will take for all lights to blink together  = LCM of 6, 72, 120 = 360 seconds

Therefore, the lights will blink together after every 360 seconds
 

Well explained 👍

FAQs on Least Common Multiple of 6,72, and 120

1.What is the GCF of 72 and 120?

2.What is the LCM of 72,90, and 120?

Therefore, LCM of 72,90 and 120.


LCM = 2×3×51


LCM = 8×9×5 =360 
 

3.How to find the GCF of 60, 72, 120?

GCF means:  multiplying all the factors of both lists. Here the GCF of 60, 72, and 120 is 360. So the GCF is 12. The steps included for the GCF calculation are as follows, first, we find out the prime factors of each number. Finally, we make sure the multiples multiply the lowest power of a common prime number.
 

4.What is the LCM of 60, 72, and 108?

LCM: The least common multiple of these numbers is 60, 72, and 108 is 1080. Multiply the highest power of these primes.
 

5.What is the GCF of 6,72 and 120 by prime factorization?

Prime factorization of each number is;


6: 2×3
72: 2×2×2×3×3 
120: 2×2×2×3×5


Accordingly, 6,72,120 are prime factors. Here, the GCF of 6, 72, and 120 is 2 × 3 = 6
 

Important Glossaries for LCM of 6, 72, and 120

  • Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, only common factors are 1 and the number itself.
  • Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8 and 10. 
  • Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.

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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.