LCM of 36 and 81 is 324. LCM is a very crucial topic in Mathematics and has a huge application in our day to day activities. The least common multiple of 36 and 81 is the value we get from the common multiples. (36, 72, 108, 144, 180, 216, ….) and (81, 162, 243, 324, 405, 486, 567, …..) are the first few multiples of 36 and 81. The LCM value can be found with the help of division, prime factorisation and by listing the multiples.
Also read: Least common multiple
What is LCM of 36 and 81?
The answer to this question is 324. The LCM of 36 and 81 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 81, is the smallest positive integer 324 which is divisible by both 36 and 81 with no remainder.
How to Find LCM of 36 and 81?
LCM of 36 and 81 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 81 Using Prime Factorisation Method
The prime factorisation of 36 and 81, respectively, is given by:
36 = 2 x 2 x 3 x 3 = 2² x 3²
81 = 3 x 3 x 3 x 3 = 3⁴
LCM (36, 81) = 324
LCM of 36 and 81 Using Division Method
We’ll divide the numbers (36, 81) by their prime factors to get the LCM of 36 and 81 using the division method (preferably common). The LCM of 36 and 81 is calculated by multiplying these divisors.
|
2 |
36 |
81 |
|
2 |
18 |
81 |
|
3 |
9 |
81 |
|
3 |
3 |
27 |
|
3 |
1 |
9 |
|
3 |
1 |
3 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (36, 81) = 324
LCM of 36 and 81 Using Listing the Multiples
To calculate the LCM of 36 and 81 by listing out the common multiples, list the multiples as shown below
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, ….
Multiples of 81 = 81, 162, 243, 324, 405, 486, …..
The smallest common multiple of 36 and 81 is 324.
Therefore LCM (36, 81) = 324
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LCM of 36 and 81 Solved Examples
Question: The LCM and GCD of two numbers are 324 and 9. If 36 is one number, find the other.
Solution:
Consider a as one number
LCM x GCD = 36 x a
a = (LCM x GCD)/36
a = (324 x 9)/36
a = 81
Hence, the other number is 81.
Frequently Asked Questions on LCM of 36 and 81
Using the prime factorisation, find the LCM of 36 and 81.
Using the prime factorisation
36 = 2 x 2 x 3 x 3
81 = 3 x 3 x 3 x 3
LCM (36, 81) = 324
Which methods can be used to find the LCM of 36 and 81?
Among 120, 52, 324, 600, find the LCM of 36 and 81.
What is the LCM of 36 and 81?
Mention the relation between GCF and LCM of 36 and 81.
The relation between GCF and LCM of 36 and 81 is
GCF x LCM = 36 x 81
GCF x LCM = 2916
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