LCM of 16, 24 and 36 is 144. Students can understand how the least common multiple of 16, 24 and 36 can be calculated with the help of the common multiples. (16, 32, 48, 64, 80, ….), (24, 48, 72, 96, 120, …..) and (36, 72, 108, 144, 180,….) are the multiples of 16, 24 and 36. The LCM of two numbers is determined using the prime factorisation method, by listing out the multiples and division method.
Also read: Least common multiple
What is LCM of 16, 24 and 36?
The answer to this question is 144. The LCM of 16, 24 and 36 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 16, 24 and 36, is the smallest positive integer 144 which is divisible by both 16, 24 and 36 with no remainder.
How to Find LCM of 16, 24 and 36?
LCM of 16, 24 and 36 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16, 24 and 36 Using Prime Factorisation Method
The prime factorisation of 16, 24 and 36, respectively, is given by:
16 = 2 × 2 × 2 × 2 = 2⁴
24 = 2 × 2 × 2 × 3 = 2³ × 3¹
36 = 2 × 2 × 3 × 3 = 2²× 3²
LCM (16, 24, 36) = 144
LCM of 16, 24 and 36 Using Division Method
We’ll divide the numbers (16, 24, 36) by their prime factors to get the LCM of 16, 24 and 36 using the division method (preferably common). The LCM of 16, 24 and 36 is calculated by multiplying these divisors.
|
2 |
16 |
24 |
36 |
|
2 |
4 |
12 |
18 |
|
2 |
2 |
6 |
9 |
|
3 |
1 |
3 |
9 |
|
3 |
1 |
1 |
3 |
|
× |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (16, 24, 36) = 144
LCM of 16, 24 and 36 Using Listing the Multiples
To calculate the LCM of 16, 24 and 36 by listing out the common multiples, list the multiples as shown below
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, ….
Multiples of 24 = 24, 48, 72, 96, 120, 144, ……
Multiples of 36 = 36, 72, 108, 144, 180, …..
LCM (16, 24, 36) = 144
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 16, 24 and 36 Solved Examples
Question: Find the smallest number divisible exactly by 16, 24 and 36.
Solution:
We know that
The smallest number exactly divisible by 16, 24 and 36 is the LCM.
(16, 32, 48, 64, 80, 96, 112, 128, 144, ….) are the multiples of 16
(24, 48, 72, 96, 120, 144, ……) are the multiples of 24
(36, 72, 108, 144, 180, …..) are the multiples of 36
Hence, the LCM of 16, 24 and 36 is 144.
Frequently Asked Questions on LCM of 16, 24 and 36
In the numbers 12, 18, 144, 156, what is the LCM of 16, 24 and 36?
List the methods used to determine the LCM of 16, 24 and 36.
The methods used to determine the LCM of 16, 24 and 36 are Prime factorisation, Division and Listing the multiples
Mention the relation between GCF and LCM of 16, 24 and 36.
The relation between GCF and LCM of 16, 24 and 36 is
LCM x GCF = 16 × 24 × 36
LCM x GCF = 13824
What is the LCM of 16, 24 and 36?
Calculate the LCM of 16, 24 and 36 using prime factorisation.
The LCM can be determined using prime factorisation method
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Hence, the LCM is 144.
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