LCM of 32 and 45

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.

Lcm Of 32 And 45

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

Related Articles

Video Lesson on Applications of LCM

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

Q1

What is the LCM of 32 and 45?

The LCM of 32 and 45 is 1440. To find the LCM of 32 and 45, we need to find the multiples of 32 and 45 (multiples of 32 = 32, 64, 96, 128 . . . . 1440; multiples of 45 = 45, 90, 135, 180 . . . . 1440) and choose the smallest multiple that is exactly divisible by 32 and 45, i.e., 1440.
Q2

List the methods used to find the LCM of 32 and 45.

The methods used to find the LCM of 32 and 45 are Prime Factorization Method, Division Method and Listing multiples.
Q3

If the LCM of 45 and 32 is 1440, Find its GCF.

LCM(45, 32) × GCF(45, 32) = 45 × 32
Since the LCM of 45 and 32 = 1440
⇒ 1440 × GCF(45, 32) = 1440
Therefore, the GCF = 1440/1440 = 1.
Q4

Which of the following is the LCM of 32 and 45? 2, 25, 18, 1440

The value of LCM of 32, 45 is the smallest common multiple of 32 and 45. The number satisfying the given condition is 1440.
Q5

How to Find the LCM of 32 and 45 by Prime Factorization?

To find the LCM of 32 and 45 using prime factorization, we will find the prime factors, (32 = 2 × 2 × 2 × 2 × 2) and (45 = 3 × 3 × 5). LCM of 32 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 32 and 45.
⇒ LCM of 32, 45 = 1440.

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*