LCM of 64 and 72 is 576. The number which divides 64 and 72 evenly gives the LCM. The common multiples among the two numbers will help you to find the least common multiple of 64 and 72. The multiples of 64 are (64, 128, 192, 256, ….) and the multiples of 72 are (72, 144, 216, 288, 360, …..) respectively. Students can get a clear cut knowledge of the LCM concept and methods such as prime factorisation, division and listing out the multiples as per the study materials at BYJU’S.
Also read: Least common multiple
What is LCM of 64 and 72?
The answer to this question is 576. The LCM of 64 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 64 and 72, is the smallest positive integer 576 which is divisible by both 64 and 72 with no remainder.
How to Find LCM of 64 and 72?
LCM of 64 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 64 and 72 Using Prime Factorisation Method
The prime factorisation of 64 and 72, respectively, is given by:
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
LCM (64, 72) = 576
LCM of 64 and 72 Using Division Method
We’ll divide the numbers (64, 72) by their prime factors to get the LCM of 64 and 72 using the division method (preferably common). The LCM of 64 and 72 is calculated by multiplying these divisors.
| 2 | 64 | 72 |
| 2 | 32 | 36 |
| 2 | 16 | 18 |
| 2 | 8 | 9 |
| 2 | 4 | 9 |
| 2 | 2 | 9 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (64, 72) = 576
LCM of 64 and 72 Using Listing the Multiples
To calculate the LCM of 64 and 72 by listing out the common multiples, list the multiples as shown below.
| Multiples of 64 | Multiples of 72 |
| 64 | 72 |
| 128 | 144 |
| 192 | 216 |
| 256 | 288 |
| 320 | 360 |
| 384 | 432 |
| 448 | 504 |
| 512 | 576 |
| 576 | 648 |
| 640 | 720 |
LCM (64, 72) = 576
Related Articles
Video Lesson on Applications of LCM
LCM of 64 and 72 Solved Examples
Determine the smallest number divisible by 64 and 72 exactly.
Solution:
The smallest number divisible by 64 and 72 exactly is LCM.
Multiples of 64 = 64, 128, 192, 256, 320, 384, ….
Multiples of 72 = 72, 144, 216, 288, 360, 432, ….
Therefore, the LCM of 64 and 72 is 576.
Frequently Asked Questions on LCM of 64 and 72
Find the GCF if the LCM of 64 and 72 is 576.
We know that,
LCM x GCF = 64 x 72
As LCM (64, 72) is 576
576 x GCF = 4608
GCF = 4608/576 = 8
Find the LCM of 64 and 72.
The LCM of 64 and 72 is 576. First the multiples of 64 and 72 have to be found to get the LCM value.
Multiples of 64 = 64, 128, 192, 256, 320, 384, ……
Multiples of 72 = 72, 144, 216, 288, 360, 432, ….
The smallest multiple exactly divisible by 64 and 72 is 576.
Show the relation between GCF and LCM of 64 and 72.
The relation between GCF and LCM of 64 and 72 is
LCM x GCF = 64 x 72
LCM x GCF = 4608
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