LCM of 18, 24 and 30 is 360. The least common multiple of 18, 24 and 30 can be found effortlessly using the multiples of each number. The multiples of 18 are (18, 36, 54, 72, 90, ….), the multiples of 24 are (24, 48, 72, 96, 120, 144, …..) and the multiples of 30 are (30, 60, 90, 120, 150, …..) respectively. For a perfect idea of the LCM concept and the methods such as prime factorisation, division and listing of the multiples refer to the materials given at BYJU’S.
Also read: Least common multiple
What is LCM of 18, 24 and 30?
The answer to this question is 360. The LCM of 18, 24 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18, 24 and 30, is the smallest positive integer 360 which is divisible by both 18, 24 and 30 with no remainder.
How to Find LCM of 18, 24 and 30?
LCM of 18, 24 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18, 24 and 30 Using Prime Factorisation Method
The prime factorisation of 18, 24 and 30, respectively, is given by:
18 = 2 x 3 x 3 = 2¹ x 3²
24 = 2 x 2 x 2 x 3 = 2³ x 3¹
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
LCM (18, 24, 30) = 360
LCM of 18, 24 and 30 Using Division Method
We’ll divide the numbers (18, 24, 30) by their prime factors to get the LCM of 18, 24 and 30 using the division method (preferably common). The LCM of 18, 24 and 30 is calculated by multiplying these divisors.
|
2 |
18 |
24 |
30 |
|
2 |
9 |
12 |
15 |
|
2 |
9 |
6 |
15 |
|
3 |
9 |
3 |
15 |
|
3 |
3 |
1 |
5 |
|
5 |
1 |
1 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (18, 24, 30) = 360
LCM of 18, 24 and 30 Using Listing the Multiples
To calculate the LCM of 18, 24 and 30 by listing out the common multiples, list the multiples as shown below.
- Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, . . . ., 288, 306, 324, 342, 360, . . . .
- Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, . . . ., 312, 336, 360, . . . .
- Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, . . . ., 240, 270, 300, 330, 360, . . . .
LCM (18, 24, 30) = 360
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Video Lesson on Applications of LCM
LCM of 18, 24 and 30 Solved Examples
Question: In 100, 16, 360, 25, find the LCM of 18, 24 and 30.
Solution:
The LCM value of 18, 24 and 30 is the smallest common multiple which is divisible evenly by the given numbers.
The value which satisfies this condition is 360.
Therefore, the LCM of 18, 24 and 30 is 360.
Frequently Asked Questions on LCM of 18, 24 and 30
Find the GCF if the LCM of 18, 24 and 30 is 360.
We know that
LCM x GCF = 18 x 24 x 36
As LCM (18, 24, 36) is 360
360 x GCF = 12960
GCF = 12960/360 = 36
What is the LCM of 18, 24 and 30?
Show the relation between GCF and LCM of 18, 24 and 30.
The relation between GCF and LCM of 18, 24 and 30 is:
LCM x GCF = 18 x 24 x 30
LCM x GCF =12960
What are the methods used to get the LCM of 18, 24 and 30?
With the help of prime factorisation, find the LCM of 18, 24 and 30.
With the help of prime factorisation
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
30 = 2 x 3 x 5
LCM of 18, 24 and 30 is 360.
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