LCM of 15, 20 and 30 is 60. Considering the multiples of 15, 20 and 30, the value evenly divisible by 15, 20 and 30 gives the LCM value. Least common multiple of 15, 20 and 30 is the common multiple we get using the multiplication operation. (15, 30, 45, 60, 75, ….), (20, 40, 60, 80, 100, …..) and (30, 60, 90, 120, 150, 180, ….) are the multiples of 15, 20 and 30. Students can grasp how the LCM of two numbers is determined using the methods such as listing multiples, prime factorization and division.
Also read: Least common multiple
What is LCM of 15, 20 and 30?
The answer to this question is 60. The LCM of 15, 20 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 15, 20 and 30, is the smallest positive integer 60 which is divisible by both 15, 20 and 30 with no remainder.
How to Find LCM of 15, 20 and 30?
LCM of 15, 20 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15, 20 and 30 Using Prime Factorisation Method
The prime factorisation of 15, 20 and 30, respectively, is given by:
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
LCM (15, 20, 30) = 60
LCM of 15, 20 and 30 Using Division Method
We’ll divide the numbers (15, 20, 30) by their prime factors to get the LCM of 15, 20 and 30 using the division method (preferably common). The LCM of 15, 20 and 30 is calculated by multiplying these divisors.
|
2 |
15 |
20 |
30 |
|
2 |
15 |
10 |
15 |
|
3 |
15 |
5 |
15 |
|
5 |
5 |
5 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (15, 20, 30) = 60
LCM of 15, 20 and 30 Using Listing the Multiples
To calculate the LCM of 15, 20 and 30 by listing out the common multiples, list the multiples as shown below
|
Multiples of 15 |
Multiples of 20 |
Multiples of 30 |
|
15 |
20 |
30 |
|
30 |
40 |
60 |
|
45 |
60 |
90 |
|
60 |
80 |
120 |
|
75 |
100 |
150 |
LCM (15, 20, 30) = 60
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 15, 20 and 30 Solved Examples
Question: What is the smallest number divisible exactly by 15, 20 and 30?
Solution:
We know that
LCM is the smallest number exactly divisible by 15, 20 and 30.
Multiples of 15 = 15, 30, 45, 60, 75, ….
Multiples of 20 = 20, 40, 60, 80, 100, …..
Multiples of 30 = 30, 60, 90, 120, 150, …..
Hence, the LCM of 15, 20 and 30 is 60.
Frequently Asked Questions on LCM of 15, 20 and 30
What are the methods used to find the LCM of 15, 20 and 30?
The methods used to find the LCM of 15, 20 and 30 are
Prime Factorisation
Division method
Listing the multiples
With the help of the prime factorisation, find the LCM of 15, 20 and 30.
First we have to know the factors in order to find the LCM
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
LCM is the product of prime factors raised to the highest exponent among 15, 20 and 30.
LCM of 15, 20 and 30 = 60
Find the GCF if the LCM of 15, 20 and 30 is 60.
LCM x GCF = 15 x 20 x 30
As the LCM = 60
60 x GCF = 9000
GCF = 9000/60 = 150
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