LCM of 72 and 120 is 360. By referring to the multiples of 72 and 120, the number which is evenly divisible by 72 and 120 gives the LCM. Least common multiple of 72 and 120 is the multiple which is commonly obtained using the multiplication operation. (72, 144, 216, 288, 360, ….) and (120, 240, 360, 480, 600, ….) are the multiples of 72 and 120. Students can know the steps used to determine the LCM of two numbers with the help of listing multiples, prime factorization and division methods.
Also read: Least common multiple
What is LCM of 72 and 120?
The answer to this question is 360. The LCM of 72 and 120 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 72 and 120, is the smallest positive integer 360 which is divisible by both 72 and 120 with no remainder.
How to Find LCM of 72 and 120?
LCM of 72 and 120 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 72 and 120 Using Prime Factorisation Method
The prime factorisation of 72 and 120, respectively, is given by:
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
120 = 2 x 2 x 2 x 3 x 5 = 2³ x 3¹ x 5¹
LCM (72, 120) = 360
LCM of 72 and 120 Using Division Method
We’ll divide the numbers (72, 120) by their prime factors to get the LCM of 72 and 120 using the division method (preferably common). The LCM of 72 and 120 is calculated by multiplying these divisors.
|
2 |
72 |
120 |
|
2 |
36 |
60 |
|
2 |
18 |
30 |
|
3 |
9 |
15 |
|
3 |
3 |
5 |
|
5 |
1 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (72, 120) = 360
LCM of 72 and 120 Using Listing the Multiples
To calculate the LCM of 72 and 120 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 72 |
Multiples of 120 |
|
72 |
120 |
|
144 |
240 |
|
216 |
360 |
|
288 |
480 |
|
360 |
600 |
LCM (72, 120) = 360
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 72 and 120 Solved Examples
Find the smallest number exactly divisible by 72 and 120.
Solution:
We know that
LCM is the smallest number exactly divisible by 72 and 120.
Multiples of 72 = 72, 144, 216, 288, 360, ….
Multiples of 120 = 120, 240, 360, 480, 600, …..
Hence, the LCM of 72 and 120 is 360.
Frequently Asked Questions on LCM of 72 and 120
Which methods are used to determine the LCM of 72 and 120?
The methods used to determine the LCM of 72 and 120 are
Prime Factorisation
Division method
Listing the multiples
Using the prime factorisation method, find the LCM of 72 and 120.
First we have to know the factors to find the LCM
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
120 = 2 x 2 x 2 x 3 x 5 = 2³ x 3¹ x 5¹
LCM is the product of prime factors raised to the highest exponent among 72 and 120.
LCM of 72 and 120 = 360
Find the GCF if the LCM of 72 and 120 is 360.
LCM x GCF = 72 x 120
As the LCM = 360
360 x GCF = 8640
GCF = 8640/360 = 24
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