LCM of 32 and 37 is 1184. The smallest number among all common multiples of 32 and 37 is LCM of 32 and 37. The LCM of any two integers is the value that is evenly divisible by the provided two numbers in mathematics. (32, 64, 96, 128, 160,… ) and (37, 74, 111, 148, 185, 222,… ) are the first few multiples of 32 and 37, respectively. To find the LCM of 32 and 37, you can use one of three methods: listing multiples, prime factorization, or the division method.
Also read: Least common multiple
What is LCM of 32 and 37?
The answer to this question is 1184. The LCM of 32 and 37 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 32 and 37, is the smallest positive integer 1184 which is divisible by both 32 and 37 with no remainder.
How to Find LCM of 32 and 37?
LCM of 32 and 37 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 32 and 37 Using Prime Factorisation Method
The prime factorisation of 32 and 37, respectively, is given by:
32 = (2 × 2 × 2 × 2 × 2) = 25 and
(37) = 371
LCM (32, 37) = 1184
LCM of 32 and 37 Using Division Method
We’ll divide the numbers (32, 37) by their prime factors to get the LCM of 32 and 37 using the division method (preferably common). The LCM of 32 and 37 is calculated by multiplying these divisors.
| 2 | 32 | 37 |
| 2 | 16 | 37 |
| 2 | 8 | 37 |
| 2 | 4 | 37 |
| 2 | 2 | 37 |
| 37 | 1 | 37 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (32, 37) = 1184
LCM of 32 and 37 Using Listing the Multiples
To calculate the LCM of 32 and 37 by listing out the common multiples, list the multiples as shown below
| Multiples of 32 | Multiples of 37 |
| 32 | 37 |
| 64 | 74 |
| 96 | 111 |
| …… | ….. |
| 1184 | 1184 |
The smallest common multiple of 32 and 37 is 1184.
Therefore LCM (32, 37) = 1184
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LCM of 32 and 37 Solved Example
Question: The product of two numbers is 1184. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 1184
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1184/1
Therefore, the LCM is 1184.
The probable combination for the given case is LCM(32, 37) = 1184.
Frequently Asked Questions on LCM of 32 and 37
What is the LCM of 32 and 37?
List the methods used to find the LCM of 32 and 37.
If the LCM of 37 and 32 is 1184, Find its GCF.
Since the LCM of 37 and 32 = 1184
⇒ 1184 × GCF(37, 32) = 1184
Therefore, the GCF (greatest common factor) = 1184/1184 = 1.
What is the Least Perfect Square Divisible by 32 and 37?
LCM of 32 and 37 = 2 × 2 × 2 × 2 × 2 × 37 [Incomplete pair(s): 2, 37] ⇒ Least perfect square divisible by each 32 and 37 = LCM(32, 37) × 2 × 37 = 87616 [Square root of 87616 = √87616 = ±296] Therefore, 87616 is the required number.
How to Find the LCM of 32 and 37 by Prime Factorization?
⇒ LCM of 32, 37 = 25 × 37 = 1184.
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