LCM of 36 and 60 is 180. Students will learn how the LCM of 36 and 60 can be found by referring to this article. The least common multiple value of 36 and 60 is the smallest number divisible evenly by the given two numbers. The multiples of 36 are (36, 72, 108, 144, 180, 216, ….) and the multiples of 60 are (60, 120, 180, 240, 300, 360, ….) respectively. Division method, Prime factorisation method and listing of the multiples are the common methods used to determine the LCM.
Also read: Least common multiple
What is LCM of 36 and 60?
The answer to this question is 180. The LCM of 36 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 60, is the smallest positive integer 180 which is divisible by both 36 and 60 with no remainder.
How to Find LCM of 36 and 60?
LCM of 36 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 60 Using Prime Factorisation Method
The prime factorisation of 36 and 60, respectively, is given by:
36 = 2 x 2 x 3 x 3 = 2² x 3²
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
LCM (36, 60) = 180
LCM of 36 and 60 Using Division Method
We’ll divide the numbers (36, 60) by their prime factors to get the LCM of 36 and 60 using the division method (preferably common). The LCM of 36 and 60 is calculated by multiplying these divisors.
|
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 (36, 60) = 180
LCM of 36 and 60 Using Listing the Multiples
To calculate the LCM of 36 and 60 by listing out the common multiples, list the multiples as shown below
|
Multiples of 36 |
Multiples of 60 |
|
36 |
60 |
|
72 |
120 |
|
108 |
180 |
|
144 |
240 |
|
180 |
300 |
|
216 |
360 |
LCM (36, 60) = 180
Related Articles
Video Lesson on Applications of LCM
LCM of 36 and 60 Solved Examples
Question: If the product of two numbers is 2160, calculate the LCM if the GCD is 12.
Solution:
It is given that,
GCD = 12
Product of two numbers = 2160
We know that;
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 2160/12
LCM = 180
Hence, the LCM is 180.
Frequently Asked Questions on LCM of 36 and 60
What is the LCM of 36 and 60?
We know that
Multiples of 36 = 36, 72, 108, 144, 180, 216, ….
Multiples of 60 = 60, 120, 180, 240, 300, 360, ….
The smallest multiple exactly divisible by 36 and 60 is 180.
If the LCM of 36 and 60 is 180, determine the GCF.
LCM x GCF = 36 x 60
Given
LCM of 36 and 60 is 180
180 x GCF = 2160
GCF = 2160/180 = 12
What are the methods used to find the LCM of 36 and 60?
The methods used to find the LCM of 36 and 60 are:
Division method
Prime Factorisation
Listing the multiples
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