LCM of 6, 12 and 15 is 60. Students will know how the least common multiple of 6, 12 and 15 is determined using the common multiples. The multiples of 6 are (6, 12, 18, 24, 30, 36, 42, ….), the multiples of 12 are (12, 24, 36, 48, 60, 72, …..) and the multiples of 15 are (15, 30, 45, 60, 75, ….) respectively. Prime factorisation, listing of multiples and division are the methods we can make use of to get the LCM value.
Also read: Least common multiple
What is LCM of 6, 12 and 15?
The answer to this question is 60. The LCM of 6, 12 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6, 12 and 15, is the smallest positive integer 60 which is divisible by both 6, 12 and 15 with no remainder.
How to Find LCM of 6, 12 and 15?
LCM of 6, 12 and 15 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 12 and 15 Using Prime Factorisation Method
The prime factorisation of 6, 12 and 15, respectively, is given by:
6 = 2 x 3 = 2¹ x 3¹
12 = 2 x 2 x 3 = 2² x 3¹
15 = 3 x 5 = 3¹ x 5¹
LCM (6, 12, 15) = 60
LCM of 6, 12 and 15 Using Division Method
We’ll divide the numbers (6, 12, 15) by their prime factors to get the LCM of 6, 12 and 15 using the division method (preferably common). The LCM of 6, 12 and 15 is calculated by multiplying these divisors.
|
2 |
6 |
12 |
15 |
|
2 |
3 |
6 |
15 |
|
3 |
3 |
3 |
15 |
|
5 |
1 |
1 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (6, 12, 15) = 60
LCM of 6, 12 and 15 Using Listing the Multiples
To calculate the LCM of 6, 12 and 15 by listing out the common multiples, list the multiples as shown below
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …..
Multiples of 12 = 12, 24, 36, 48, 60, 72, ……
Multiples of 15 = 15, 30, 45, 60, 75, 90, …….
LCM (6, 12, 15) = 60
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LCM of 6, 12 and 15 Solved Examples
Question: Which is the LCM of 6, 12 and 15 among 60, 18, 28, 11?
Solution:
LCM is the smallest common multiple divisible by the given three numbers.
The number which satisfies this condition is 60.
Hence, the LCM of 6, 12 and 15 is 60.
Frequently Asked Questions on LCM of 6, 12 and 15
What is the LCM of 6, 12 and 15?
What is the GCF if the LCM of 6, 12 and 15 is 60?
LCM x GCF = 6 x 12 x 15
Given
LCM of 6, 12 and 15 is 60
60 x GCF = 1080
GCF = 1080/60 = 18
List the methods used to find the LCM of 6, 12 and 15.
Using prime factorisation, find the LCM of 6, 12 and 15.
Using prime factorisation,
6 = 2 x 3
12 = 2 x 2 x 3
15 = 3 x 5
LCM of 6, 12 and 15 = 60
Determine the LCM of 6, 12 and 15.
LCM of 6, 12 and 15 can be found by listing the multiples
(6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ….) are the multiples of 6
(12, 24, 36, 48, 60, 72, ……) are the multiples of 12
(15, 30, 45, 60, 75, 90, ….) are the multiples of 15
LCM of 6, 12 and 15 is 60.
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