LCM of 12, 15 and 20 is 60. The value evenly divisible by 12, 15 and 20 gives the LCM. Students can obtain the least common multiple of 12, 15 and 20 from the common multiples of the given numbers. The multiples of 12 are (12, 24, 36, 48, 60, 72, ….), the multiples of 15 are (15, 30, 45, 60, 75, …..) and the multiples of 20 are (20, 40, 60, 80, 100, 120, ….) respectively. Prime factorisation, listing of the multiples and division are some of the most commonly used methods to determine the LCM.
Also read: Least common multiple
What is LCM of 12, 15 and 20?
The answer to this question is 60. The LCM of 12, 15 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12, 15 and 20, is the smallest positive integer 60 which is divisible by both 12, 15 and 20 with no remainder.
How to Find LCM of 12, 15 and 20?
LCM of 12, 15 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 15 and 20 Using Prime Factorisation Method
The prime factorisation of 12, 15 and 20, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
LCM (12, 15, 20) = 60
LCM of 12, 15 and 20 Using Division Method
We’ll divide the numbers (12, 15, 20) by their prime factors to get the LCM of 12, 15 and 20 using the division method (preferably common). The LCM of 12, 15 and 20 is calculated by multiplying these divisors.
|
2 |
12 |
15 |
20 |
|
2 |
6 |
15 |
10 |
|
3 |
3 |
15 |
5 |
|
5 |
1 |
5 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (12, 15, 20) = 60
LCM of 12, 15 and 20 Using Listing the Multiples
To calculate the LCM of 12, 15 and 20 by listing out the common multiples, list the multiples as shown below
|
Multiples of 12 |
Multiples of 15 |
Multiples of 20 |
|
12 |
15 |
20 |
|
24 |
30 |
40 |
|
36 |
45 |
60 |
|
48 |
60 |
80 |
|
60 |
75 |
100 |
|
72 |
90 |
120 |
|
84 |
105 |
140 |
LCM (12, 15, 20) = 60
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Video Lesson on Applications of LCM
LCM of 12, 15 and 20 Solved Examples
Question: Calculate the smallest number which is exactly divisible by 12, 15 and 20.
Solution:
The smallest number divisible by 12, 15 and 20 exactly is the LCM
Multiples of 12 = 12, 24, 36, 48, 60, 72, ….
Multiples of 15 = 15, 30, 45, 60, 75, …..
Multiples of 20 = 20, 40, 60, 80, 100, 120, ….
Hence, LCM of 12, 15 and 20 is 60.
Frequently Asked Questions on LCM of 12, 15 and 20
What is the LCM of 12, 15 and 20?
What is the GCF if the LCM of 12, 15 and 20 is 60?
LCM x GCF = 12 x 15 x 20
Given
LCM of 12, 15 and 20 is 60
60 x GCF = 3600
GCF = 3600/60 = 60
What are the methods which can be applied to find the LCM of 12, 15 and 20?
The methods which can be applied to find the LCM of 12, 15 and 20 are
Prime Factorisation
Division method
Listing the multiples
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