LCM of 24, 36 and 72 is 72. The number which is evenly divisible and is the smallest among the multiples of the 24, 36 and 72 shows the LCM. From the multiples of each number, the least common multiple of 24, 36 and 72 is found. (24, 48, 72, 96, 120, ….), (36, 72, 108, 144, 180, …..) and (72, 144, 216, 288, 360,….) are the multiples of 24, 36 and 72. The LCM of 24, 36 and 72 can be found using the prime factorisation method, division method and listing the multiples.
Also read: Least common multiple
What is LCM of 24, 36 and 72?
The answer to this question is 72. The LCM of 24, 36 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24, 36 and 72, is the smallest positive integer 72 which is divisible by both 24, 36 and 72 with no remainder.
How to Find LCM of 24, 36 and 72?
LCM of 24, 36 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24, 36 and 72 Using Prime Factorisation Method
The prime factorisation of 24, 36 and 72, respectively, is given by:
24 = 2 x 2 x 2 x 3 = 2³x 3¹
36 = 2 x 2 x 3 x 3 = 2² x 3²
72 = 2 x 2 x 2 x 3 x 3 = 2³x 3²
LCM (24, 36, 72) = 80
LCM of 24, 36 and 72 Using Division Method
We’ll divide the numbers (24, 36, 72) by their prime factors to get the LCM of 24, 36 and 72 using the division method (preferably common). The LCM of 24, 36 and 72 is calculated by multiplying these divisors.
|
2 |
24 |
36 |
72 |
|
2 |
12 |
18 |
36 |
|
2 |
6 |
9 |
18 |
|
3 |
3 |
9 |
9 |
|
3 |
1 |
3 |
3 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (24, 36, 72) = 72
LCM of 24, 36 and 72 Using Listing the Multiples
To calculate the LCM of 24, 36 and 72 by listing out the common multiples, list the multiples as shown below
|
Multiples of 24 |
Multiples of 36 |
Multiples of 72 |
|
24 |
36 |
72 |
|
48 |
72 |
144 |
|
72 |
108 |
216 |
|
96 |
144 |
288 |
LCM (24, 36, 72) = 72
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LCM of 24, 36 and 72 Solved Examples
Question: What is the smallest number divisible exactly by 24, 36 and 72?
Solution:
The smallest number divisible exactly by 24, 36 and 72 is the LCM
Multiples of 24 = 24, 48, 72, 96, …..
Multiples of 36 = 36, 78, 108, 144, ….
Multiples of 72 = 72, 144, 216, 288, …..
Hence, the LCM is 72.
Frequently Asked Questions on LCM of 24, 36 and 72
What is the LCM of 24, 36 and 72?
List the methods which can be used to get the LCM value of 24, 36 and 72.
What is the GCF if the LCM of 24, 36 and 72 is 72?
LCM x GCF = 24 x 36 x 72
Given
LCM of 24, 36 and 72 = 72
72 x GCF = 62208
GCF = 62208/72 = 864
In 81, 18, 72, 11, find the LCM of 24, 36 and 72.
Determine the LCM of 24, 36 and 72 using prime factorisation.
Using prime factorisation
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
72 = 2 x 2 x 2 x 3 x 3
LCM of 24, 36 and 72 is 72.
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