LCM of 5, 6 and 10 is 30. Memorizing the steps to find the least common multiple of 5, 6 and 10 is easy for the students using this article. (5, 10, 15, 20, 25, 30, 35, ….), (6, 12, 18, 24, 30, 36, 42, …..) and (10, 20, 30, 40, 50, 60, 70,….) are the multiples of 5, 6 and 10. We can use methods like prime factorisation, listing the multiples and division to find the LCM of two numbers.
Also read: Least common multiple
What is LCM of 5, 6 and 10?
The answer to this question is 30. The LCM of 5, 6 and 10 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 5, 6 and 10, is the smallest positive integer 30 which is divisible by both 5, 6 and 10 with no remainder.
How to Find LCM of 5, 6 and 10?
LCM of 5, 6 and 10 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 6 and 10 Using Prime Factorisation Method
The prime factorisation of 5, 6 and 10, respectively, is given by:
5 = 5¹
6 = 2 x 3 = 2¹ x 3¹
10 = 2 x 5 = 2¹ x 5¹
LCM (5, 6, 10) = 30
LCM of 5, 6 and 10 Using Division Method
We’ll divide the numbers (5, 6, 10) by their prime factors to get the LCM of 5, 6 and 10 using the division method (preferably common). The LCM of 5, 6 and 10 is calculated by multiplying these divisors.
|
2 |
5 |
6 |
10 |
|
3 |
5 |
3 |
5 |
|
5 |
5 |
1 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (5, 6, 10) = 30
LCM of 5, 6 and 10 Using Listing the Multiples
To calculate the LCM of 5, 6 and 10 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 5 |
Multiples of 6 |
Multiples of 10 |
|
5 |
6 |
10 |
|
10 |
12 |
20 |
|
15 |
18 |
30 |
|
20 |
24 |
40 |
|
25 |
30 |
50 |
|
30 |
36 |
60 |
|
35 |
42 |
70 |
LCM (5, 6, 10) = 30
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 5, 6 and 10 Solved Examples
Question: Calculate the smallest number which is exactly divisible by 5, 6 and 10.
Solution:
The smallest number which is exactly divisible by 5, 6 and 10 is the LCM value
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, ….
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, ….
Multiples of 10 = 10, 20, 30, 40, 50, 60, …..
Hence, the LCM is 30.
Frequently Asked Questions on LCM of 5, 6 and 10
From the numbers 35, 48, 62, 30, 21, what is the LCM of 5, 6 and 10?
Which are the methods used to determine the LCM of 5, 6 and 10?
The methods used to determine the LCM of 5, 6 and 10 are
Prime factorisation
Division
Listing the multiples
Show the relation between GCF and LCM of 5, 6 and 10.
The relation between GCF and LCM of 5, 6 and 10 is
LCM x GCF = 30 x 42
LCM x GCF = 1260
What is the LCM of 5, 6 and 10?
Write the relation between GCF and LCM of 5, 6 and 10.
The relation between GCF and LCM of 5, 6 and 10 is
GCF x LCM = 5 x 6 x 10
GCF x LCM = 300
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