LCM of 45 and 72 is 360. Students can get the Least common multiple value of 45 and 72 from the common multiples. (45, 90, 135, 180, 225, 270, 315, ….) and (72, 144, 216, 288, 360, 432, 504, ,….) are the multiples of 45 and 72. The methods used to get the LCM of two numbers are prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 45 and 72?
The answer to this question is 360. The LCM of 45 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 45 and 72, is the smallest positive integer 360 which is divisible by both 45 and 72 with no remainder.
How to Find LCM of 45 and 72?
LCM of 45 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 45 and 72 Using Prime Factorisation Method
The prime factorisation of 45 and 72, respectively, is given by:
45 = 3 x 3 x 5 = 3²x 5¹
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
LCM (45, 72) = 360
LCM of 45 and 72 Using Division Method
We’ll divide the numbers (45, 72) by their prime factors to get the LCM of 45 and 72 using the division method (preferably common). The LCM of 45 and 72 is calculated by multiplying these divisors.
|
2 |
45 |
72 |
|
2 |
45 |
36 |
|
2 |
45 |
18 |
|
3 |
45 |
9 |
|
3 |
15 |
3 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (45, 72) = 360
LCM of 45 and 72 Using Listing the Multiples
To calculate the LCM of 45 and 72 by listing out the common multiples, list the multiples as shown below.
Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, ….
Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, …..
LCM (45, 72) = 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 45 and 72 Solved Examples
Question: If the GCD is 9 and the product of two numbers is 3240, determine the LCM.
Solution:
Given
GCD = 9
Product = 3240
LCM x GCD = Product of two numbers
LCM = Product/ GCD
LCM = 3240/9
LCM = 360
Hence, the LCM of 45 and 72 is 360.
Frequently Asked Questions on LCM of 45 and 72
In the numbers 12, 150, 360, 180, find the LCM of 45 and 72.
Determine the GCF if the LCM of 45 and 72 is 360.
LCM x GCF = 45 x 72
Given
LCM of 45 and 72 = 360
360 x GCF = 3240
GCF = 3240/360 = 9
Show the relation between GCF and LCM of 45 and 72.
The relation between GCF and LCM of 45 and 72 is:
LCM x GCF = 45 x 72
LCM x GCF = 3240
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