LCM of 36 and 64 is 576. The common multiple evenly divisible by 36 and 64 gives the LCM value. The least common multiple of 36 and 64 can be determined by listing the common multiples using the multiplication operation. (36, 72, 108, 144, ….) and (64, 128, 192, 256, 320, 384, 448,….) are the first few multiples of 36 and 64. Various methods like prime factorisation, division and listing of multiples are used to get the LCM value.
Also read: Least common multiple
What is LCM of 36 and 64?
The answer to this question is 576. The LCM of 36 and 64 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36 and 64, is the smallest positive integer 576 which is divisible by both 36 and 64 with no remainder.
How to Find LCM of 36 and 64?
LCM of 36 and 64 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 64 Using Prime Factorisation Method
The prime factorisation of 36 and 64, respectively, is given by:
36 = 2 × 2 × 3 × 3 = 2² × 3²
64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶
LCM (36, 64) = 576
LCM of 36 and 64 Using Division Method
We’ll divide the numbers (36, 64) by their prime factors to get the LCM of 36 and 64 using the division method (preferably common). The LCM of 36 and 64 is calculated by multiplying these divisors.
|
2 |
36 |
64 |
|
2 |
18 |
32 |
|
2 |
9 |
16 |
|
2 |
9 |
8 |
|
2 |
9 |
4 |
|
2 |
9 |
2 |
|
3 |
9 |
1 |
|
3 |
3 |
1 |
|
× |
1 |
1 |
No further division can be done.
Hence, LCM (36, 64) = 576
LCM of 36 and 64 Using Listing the Multiples
To calculate the LCM of 36 and 64 by listing out the common multiples, list the multiples as shown below:
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 468, 504, 540, 576, ….
Multiples of 64 = 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, . . . ., 384, 448, 512, 576, …..
LCM (36, 64) = 576
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Video Lesson on Applications of LCM
LCM of 36 and 64 Solved Examples
Question: Find the LCM if the product of two numbers is 2304 and the GCD is 4.
Solution:
It is given that
Product of two numbers = 2304
GCD = 4
We know that,
LCM × GCD = Product of two numbers
LCM = Product/GCD
LCM = 2304/4
LCM = 576
Hence, the LCM is 576.
Frequently Asked Questions on LCM of 36 and 64
Find the LCM of 36 and 64.
What methods can be used to find the LCM of 36 and 64?
Find the GCF if the LCM of 36 and 64 is 576.
LCM × GCF = 36 × 64
Given
LCM of 36 and 64 = 576
576 × GCF = 2304
GCF = 2304/576 = 4
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