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141 LearnersLast updated on December 24th, 2024
LCM OF 6,72 AND 120
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.
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
LCM OF 6, 72, and 120 Examples
Problem 1
Find x LCM (6,72,x) = 360?
Explanation
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?
Explanation
Problem 3
Find the smallest number that is exactly divisible by 6,72, and 120.
Explanation
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?
Explanation
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?
Explanation
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?
3.How to find the GCF of 60, 72, 120?
4.What is the LCM of 60, 72, and 108?
5.What is the GCF of 6,72 and 120 by prime factorization?
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.
