LCM of 12 and 36 is 36. Students will be able to learn how the least common multiple of 12 and 36 can be obtained from the common multiples. (12, 24, 36, 48, 60, 72, ….) and (36, 72, 108, 144, 180,….) are the multiples of 12 and 36. The methods which can be used to determine the LCM of two numbers are prime factorisation, by listing the multiples and division.
Also read: Least common multiple
What is LCM of 12 and 36?
The answer to this question is 36. The LCM of 12 and 36 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 36, is the smallest positive integer 36 which is divisible by both 12 and 36 with no remainder.
How to Find LCM of 12 and 36?
LCM of 12 and 36 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 36 Using Prime Factorisation Method
The prime factorisation of 12 and 36, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
36 = 2 x 2 x 3 x 3 = 2² x 3²
LCM (12, 36) = 36
LCM of 12 and 36 Using Division Method
We’ll divide the numbers (12, 36) by their prime factors to get the LCM of 12 and 36 using the division method (preferably common). The LCM of 12 and 36 is calculated by multiplying these divisors.
| 2 | 12 | 36 |
| 2 | 6 | 18 |
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 36) = 36
LCM of 12 and 36 Using Listing the Multiples
To calculate the LCM of 12 and 36 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 36 |
| 12 | 36 |
| 24 | 72 |
| 36 | 108 |
| 48 | 144 |
| 60 | – |
| 72 | – |
LCM (12, 36) = 36
Related Articles
Video Lesson on Applications of LCM
LCM of 12 and 36 Solved Example
Question: Determine the smallest number divisible by 12 and 36 exactly.
Solution:
We know that,
The smallest number exactly divisible by 12 and 36 is the LCM.
Multiples of 12 = 12, 24, 36, 48, 60,…..
Multiples of 36 = 36, 72, 108, 144
Hence, the LCM of 12 and 36 is 36.
Frequently Asked Questions on LCM of 12 and 36
In the numbers 2, 25, 5, 36, find the LCM of 12 and 36.
Find the GCF if the LCM of 12 and 36 is 36.
LCM x GCF = 12 x 36
Given
LCM of 12 and 36 = 36
36 x GCF = 432
GCF = 432/36 = 12
Write the relation between GCF and LCM of 12 and 36.
The relation between GCF and LCM of 12 and 36 is
LCM x GCF = 12 x 36
LCM x GCF = 432
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