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