LCM of 36 and 72 is 72. The common multiple divisible evenly by the numbers 36 and 72 is the LCM. Students can learn to get the least common multiples of 36 and 72 from the common multiples. (36, 72, 108, 144, 180, 216, 252, ….) and (72, 144, 216, 288, 360, 432, ….) are the multiples of 36 and 72. The LCM of two numbers can be found using methods like listing the multiples, prime factorization and division method.
Also read: Least common multiple
What is LCM of 36 and 72?
The answer to this question is 72. The LCM of 36 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 72, is the smallest positive integer 72 which is divisible by both 36 and 72 with no remainder.
How to Find LCM of 36 and 72?
LCM of 36 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 72 Using Prime Factorisation Method
The prime factorisation of 36 and 72, respectively, is given by:
36 = 2 x 2 x 3 x 3 = 2² x 3²
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
LCM (36, 72) = 72
LCM of 36 and 72 Using Division Method
We’ll divide the numbers (36, 72) by their prime factors to get the LCM of 36 and 72 using the division method (preferably common). The LCM of 36 and 72 is calculated by multiplying these divisors.
| 2 | 36 | 72 |
| 2 | 18 | 36 |
| 2 | 9 | 18 |
| 3 | 9 | 9 |
| 3 | 3 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (36, 72) = 72
LCM of 36 and 72 Using Listing the Multiples
To calculate the LCM of 36 and 72 by listing out the common multiples, list the multiples as shown below
| Multiples of 36 | Multiples of 72 |
| 36 | 72 |
| 72 | 144 |
| 108 | 216 |
| 144 | – |
LCM (36, 72) = 72
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Video Lesson on Applications of LCM
LCM of 36 and 72 Solved Example
Find the smallest number exactly divisible by 36 and 72.
Solution:
We know that
LCM is the smallest number exactly divisible by 36 and 72.
Multiples of 36 = 36, 72, 108, 144, ….
Multiples of 72 = 72, 144, 216, ….
Hence, the LCM of 36 and 72 is 72.
Frequently Asked Questions on LCM of 36 and 72
How to determine the LCM of 36 and 72?
The LCM of 36 and 72 can be found using the methods below
Division method
Prime Factorisation
Listing the multiples
With the help of the prime factorisation method, determine the LCM of 36 and 72.
To get the LCM, the factors should be known
36 = 2 x 2 x 3 x 3 = 2² x 3²
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
LCM (36, 72) = 72
What is the GCF if the LCM of 36 and 72 is 72?
LCM x GCF = 36 x 72
As the LCM = 72
72 x GCF = 2592
GCF = 2592/72 = 36
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