LCM of 32 and 37

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.

lcm of 32 and 37

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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Video Lesson on Applications of LCM

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

Q1

What is the LCM of 32 and 37?

The LCM of 32 and 37 is 1184. To find the least common multiple of 32 and 37, we need to find the multiples of 32 and 37 (multiples of 32 = 32, 64, 96, 128 . . . . 1184; multiples of 37 = 37, 74, 111, 148 . . . . 1184) and choose the smallest multiple that is exactly divisible by 32 and 37, i.e., 1184.
Q2

List the methods used to find the LCM of 32 and 37.

The methods used to find the LCM of 32 and 37 are Prime Factorization Method, Division Method and Listing multiples.
Q3

If the LCM of 37 and 32 is 1184, Find its GCF.

LCM(37, 32) × GCF(37, 32) = 37 × 32
Since the LCM of 37 and 32 = 1184
⇒ 1184 × GCF(37, 32) = 1184
Therefore, the GCF (greatest common factor) = 1184/1184 = 1.
Q4

What is the Least Perfect Square Divisible by 32 and 37?

The least number divisible by 32 and 37 = LCM(32, 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.
Q5

How to Find the LCM of 32 and 37 by Prime Factorization?

To find the LCM of 32 and 37 using prime factorization, we will find the prime factors, (32 = 2 × 2 × 2 × 2 × 2) and (37 = 37). LCM of 32 and 37 is the product of prime factors raised to their respective highest exponent among the numbers 32 and 37.
⇒ LCM of 32, 37 = 25 × 37 = 1184.

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