LCM of 20, 30 and 60 is 60. You will understand how the Least common multiple 20, 30 and 60 is found by considering the common multiples. (20, 40, 60, 80, 100, 120, ….), (30, 60, 90, 120, 150, ……) and (60, 120, 180, 240, 300, ,….) are the multiples of 20, 30 and 60. The methods we can use to get the LCM of two numbers are prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 20, 30 and 60?
The answer to this question is 60. The LCM of 20, 30 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 20, 30 and 60, is the smallest positive integer 60 which is divisible by both 20, 30 and 60 with no remainder.
How to Find LCM of 20, 30 and 60?
LCM of 20, 30 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20, 30 and 60 Using Prime Factorisation Method
The prime factorisation of 20, 30 and 60, respectively, is given by:
20 = 2 x 2 x 5 = 2²x 5¹
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
60 = 2 x 2 x 3 x 5 = 2²x 3¹ x 5¹
LCM (20, 30, 60) = 60
LCM of 20, 30 and 60 Using Division Method
We’ll divide the numbers (20, 30, 60) by their prime factors to get the LCM of 20, 30 and 60 using the division method (preferably common). The LCM of 20, 30 and 60 is calculated by multiplying these divisors.
|
2 |
20 |
30 |
60 |
|
2 |
10 |
15 |
30 |
|
3 |
5 |
15 |
15 |
|
5 |
5 |
5 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (20, 30, 60) = 60
LCM of 20, 30 and 60 Using Listing the Multiples
To calculate the LCM of 20, 30 and 60 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 20 |
Multiples of 30 |
Multiples of 60 |
|
20 |
30 |
60 |
|
40 |
60 |
120 |
|
60 |
90 |
180 |
|
80 |
120 |
240 |
|
100 |
150 |
300 |
LCM (20, 30, 60) = 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 20, 30 and 60 Solved Examples
Question: If the GCD is 600 and the product of three numbers is 36000, determine the LCM.
Solution:
Given
GCD = 600
Product = 36000
LCM x GCD = Product of two numbers
LCM = Product/ GCD
LCM = 36000/600
LCM = 60
Hence, the LCM of 20, 30 and 60 is 60.
Frequently Asked Questions on LCM of 20, 30 and 60
In the numbers 120, 150, 60, 130, find the LCM of 20, 30 and 60.
Determine the GCF if the LCM of 20, 30 and 60 is 60.
LCM x GCF = 20 x 30 x 60
Given
LCM of 20, 30 and 60 = 60
60 x GCF = 36000
GCF = 36000/60 = 600
Show the relation between GCF and LCM of 20, 30 and 60.
The relation between GCF and LCM of 20, 30 and 60 is:
LCM x GCF = 20 x 30 x 60
LCM x GCF = 36000
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