LCM of 16, 24, 36 and 54 is 432. The number which is divisible evenly and is the smallest among the multiples shows the LCM value. By listing the multiples, we can easily find the least common multiple of 16, 24, 36 and 54. (16, 32, 48, 64, 80, ….), (24, 48, 72, 96, 120, ….). (36, 72, 108, 144, 180, ….) and (54, 108, 162, 216, 270,….) are the multiples of 16, 24, 36 and 54. You will be able to find the LCM of 16, 24, 36 and 54 using certain methods like the prime factorisation, division and by listing out the multiples.
Also read: Least common multiple
What is LCM of 16, 24, 36 and 54?
The answer to this question is 432. The LCM of 16, 24, 36 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 16, 24, 36 and 54, is the smallest positive integer 432 which is divisible by both 16, 24, 36 and 54 with no remainder.
How to Find LCM of 16, 24, 36 and 54?
LCM of 16, 24, 36 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16, 24, 36 and 54 Using Prime Factorisation Method
The prime factorisation of 16, 24, 36 and 54, respectively, is given by:
16 = 2 x 2 x 2 x 2 = 2⁴
24 = 2 x 2 x 2 x 3 = 2³ x 3¹
36 = 2 x 2 x 3 x 3 = 2² x 3²
54 = 2 x 3 x 3 x 3 = 2¹ x 3³
LCM (16, 24, 36, 54) = 432
LCM of 16, 24, 36 and 54 Using Division Method
We’ll divide the numbers (16, 24, 36, 54) by their prime factors to get the LCM of 16, 24, 36 and 54 using the division method (preferably common). The LCM of 16, 24, 36 and 54 is calculated by multiplying these divisors.
|
2 |
16 |
24 |
36 |
54 |
|
2 |
8 |
12 |
18 |
27 |
|
2 |
4 |
6 |
9 |
27 |
|
2 |
2 |
3 |
9 |
27 |
|
3 |
1 |
3 |
9 |
27 |
|
3 |
1 |
1 |
3 |
9 |
|
3 |
1 |
1 |
1 |
3 |
|
x |
1 |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (16, 24, 36, 54) = 80
LCM of 16, 24, 36 and 54 Using Listing the Multiples
To calculate the LCM of 16, 24, 36 and 54 by listing out the common multiples, list the multiples as shown below
Multiples of 16 = 16, 32, 48, 64, 80, ….
Multiples of 24 = 24, 48, 72, 96, 120, …..
Multiples of 36 = 36, 72, 108, 144, 180, …..
Multiples of 54 = 54, 108, 162, 216, 270, …..
LCM (16, 24, 36, 54) = 432
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LCM of 16, 24, 36 and 54 Solved Examples
Question: Which is the LCM of 16, 24, 36 and 54 among the following numbers? 36, 6, 432, 25
Solution:
The LCM value is the smallest common multiple of 16, 24, 36 and 54
The number which satisfies this condition is 432
Hence, the LCM is 432.
Frequently Asked Questions on LCM of 16, 24, 36 and 54
What is the LCM of 16, 24, 36 and 54?
The LCM of 16, 24, 36 and 54 is 432.
The smallest multiple exactly divisible by 16, 24, 36 and 54 should be calculated.
Multiples of 16 = 16, 32, 48, 64, 80, ….
Multiples of 24 = 24, 48, 72, 96, 120, …..
Multiples of 36 = 36, 72, 108, 144, 180, …..
Multiples of 54 = 54, 108, 162, 216, 270, …..
The smallest common multiple exactly divisible by 16, 24, 36 and 54 is 432.
List the methods which can be used to get the LCM value of 16, 24, 36 and 54.
Using the prime factorisation method, find the LCM of 16, 24, 36 and 54.
Using the prime factorisation method
16 = 2 x 2 x 2 x 2 = 2⁴
24 = 2 x 2 x 2 x 3 = 2³ x 3¹
36 = 2 x 2 x 3 x 3 = 2² x 3²
54 = 2 x 3 x 3 x 3 = 2¹ x 3³
Therefore, the LCM is 432.
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