LCM of 6 and 20 is 60. The LCM value is the number evenly divisible by the given numbers. Least common multiple of 6 and 20 is the smallest number we obtain considering the common multiples. (6, 12, 18, 24, 30, ….) and (20, 40, 60, 80, 100,….) are the few multiples of 6 and 20. We can find the LCM easily with the help of various methods such as prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 6 and 20?
The answer to this question is 60. The LCM of 6 and 20 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 20, is the smallest positive integer 60 which is divisible by both 6 and 20 with no remainder.
How to Find LCM of 6 and 20?
LCM of 6 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 20 Using Prime Factorisation Method
The prime factorisation of 6 and 20, respectively, is given by:
6 = 2 x 3 = 2¹ x 3¹
20 = 2 x 2 x 5 = 2² x 5¹
LCM (6, 20) = 60
LCM of 6 and 20 Using Division Method
We’ll divide the numbers (6, 20) by their prime factors to get the LCM of 6 and 20 using the division method (preferably common). The LCM of 6 and 20 is calculated by multiplying these divisors.
2 | 6 | 20 |
2 | 3 | 10 |
3 | 3 | 5 |
5 | 1 | 5 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (6, 20) = 60
LCM of 6 and 20 Using Listing the Multiples
To calculate the LCM of 6 and 20 by listing out the common multiples, list the multiples as shown below
Multiples of 6 | Multiples of 20 |
6 | 20 |
12 | 40 |
18 | 60 |
24 | 80 |
30 | 100 |
36 | 120 |
42 | 140 |
48 | 160 |
54 | 180 |
60 | 200 |
66 | 220 |
The smallest common multiple of 6 and 20 is 60.
Therefore LCM (6, 20) = 60
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Video Lesson on Applications of LCM
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LCM of 6 and 20 Solved Example
Question: The LCM and GCD of two numbers are 60 and 2. If one number is 6, determine the other number.
Solution:
Consider m as the other number
GCD x LCM = 6 x m
m = (GCD x LCM)/6
m = (2 x 60)/6
m = 120/6
m = 20
Hence, the other number is 20.
Frequently Asked Questions on LCM of 6 and 20
How can the LCM of 6 and 20 be found?
What are the methods used to get the LCM value of 6 and 20?
Calculate the GCF if the LCM of 6 and 20 is 60.
LCM x GCF = 6 x 20
Given
LCM of 6 and 20 = 60
60 x GCF = 120
GCF = 120/60 = 2
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