LCM of 32 and 45 is 1440. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest number among all common multiples of 32 and 45 is the LCM of 32 and 45. (32, 64, 96, 128,… ) and (45, 90, 135, 180, 225, 270,… ) are the first few multiples of 32 and 45, respectively. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 32 and 45?
The answer to this question is 1440. The LCM of 32 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 32 and 45, is the smallest positive integer 1440 which is divisible by both 32 and 45 with no remainder.
How to Find LCM of 32 and 45?
LCM of 32 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 32 and 45 Using Prime Factorisation Method
The prime factorisation of 32 and 45, respectively, is given by:
32 = (2 × 2 × 2 × 2 × 2) = 25 and
45 = (3 × 3 × 5) = 32 × 51
LCM (32, 45) = 1440
LCM of 32 and 45 Using Division Method
We’ll divide the numbers (32, 45) by their prime factors to get the LCM of 32 and 45 using the division method (preferably common). The LCM of 32 and 45 is calculated by multiplying these divisors.
| 2 | 32 | 45 |
| 2 | 16 | 45 |
| 2 | 8 | 45 |
| 2 | 4 | 45 |
| 2 | 2 | 45 |
| 3 | 1 | 15 |
| 3 | 1 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (32, 45) = 1440
LCM of 32 and 45 Using Listing the Multiples
To calculate the LCM of 32 and 45 by listing out the common multiples, list the multiples as shown below
| Multiples of 32 | Multiples of 45 |
| 32 | 45 |
| 64 | 90 |
| 96 | 135 |
| ……. | …… |
| 1440 | 1440 |
The smallest common multiple of 32 and 45 is 1440.
Therefore LCM (32, 45) = 1440
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LCM of 32 and 45 Solved Example
The product of two numbers is 1440. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 1440
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1440/1
Therefore, the LCM is 1440.
The probable combination for the given case is LCM(32, 45) = 1440.
Frequently Asked Questions on LCM of 32 and 45
What is the LCM of 32 and 45?
List the methods used to find the LCM of 32 and 45.
If the LCM of 45 and 32 is 1440, Find its GCF.
Since the LCM of 45 and 32 = 1440
⇒ 1440 × GCF(45, 32) = 1440
Therefore, the GCF = 1440/1440 = 1.
Which of the following is the LCM of 32 and 45? 2, 25, 18, 1440
How to Find the LCM of 32 and 45 by Prime Factorization?
⇒ LCM of 32, 45 = 1440.
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