LCM of 144 and 180 is 720. In Mathematics, the LCM value is evenly divisible by the two given numbers. Least common multiples of 144 and 180 can be found by using the common multiples. (144, 288, 432, 576, 720, ….) and (180, 360, 540, 720, 900, 1080, 1260,….) are the first set of multiples of the numbers 144 and 180. The LCM can be effortlessly calculated using prime factorisation, the division method and by listing out the multiples.
Also read: Least common multiple
What is LCM of 144 and 180?
The answer to this question is 720. The LCM of 144 and 180 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 144 and 180, is the smallest positive integer 720 which is divisible by both 144 and 180 with no remainder.
How to Find LCM of 144 and 180?
LCM of 144 and 180 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 144 and 180 Using Prime Factorisation Method
The prime factorisation of 144 and 180, respectively, is given by:
144 = 2 x 2 x 2 x 2 x 3 x 3 = 2⁴ x 3²
180 = 2 x 2 x 3 x 3 x 5 = 2² x 3² x 5¹
LCM (144, 180) = 720
LCM of 144 and 180 Using Division Method
We’ll divide the numbers (144, 180) by their prime factors to get the LCM of 144 and 180 using the division method (preferably common). The LCM of 144 and 180 is calculated by multiplying these divisors.
|
2 |
144 |
180 |
|
2 |
72 |
90 |
|
2 |
36 |
45 |
|
2 |
18 |
45 |
|
3 |
9 |
45 |
|
3 |
3 |
15 |
|
5 |
1 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (144, 180) = 720
LCM of 144 and 180 Using Listing the Multiples
To calculate the LCM of 144 and 180 by listing out the common multiples, list the multiples as shown below
|
Multiples of 144 |
Multiples of 180 |
|
144 |
180 |
|
288 |
360 |
|
432 |
540 |
|
576 |
720 |
|
720 |
900 |
LCM (144, 180) = 720
Related Articles
Video Lesson on Applications of LCM
LCM of 144 and 180 Solved Examples
Question: If the product of two numbers is 25920 and the GCD is 36, find the LCM.
Solution:
It is given that
Product of two numbers = 25920
GCD = 36
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 25920/36
LCM = 720
Hence, the LCM is 720.
Frequently Asked Questions on LCM of 144 and 180
Find the LCM of 144 and 180.
Which methods can be used to get the LCM of 144 and 180?
What is the GCF if the LCM of 144 and 180 is 720?
LCM x GCF = 144 x 180
Given
LCM of 144 and 180 = 720
720 x GCF = 25920
GCF = 25920/720 = 36
What is the LCM of 144 and 180?
Show the relation between GCF and LCM of 144 and 180.
The relation between GCF and LCM of 144 and 180 is
GCF x LCM = 144 x 180
GCF x LCM = 25920
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