LCM of 32 and 60

LCM of 32 and 60 is 480. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The least common multiple (LCM) of 32 and 60 is the smallest number among all such multiples. (32, 64, 96, 128) and (60, 120, 180, 240, 300, 360, 420,.. ) are the first few multiples of 32 and 60, respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.

Also read: Least common multiple

What is LCM of 32 and 60?

The answer to this question is 480. The LCM of 32 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 32 and 60, is the smallest positive integer 480 which is divisible by both 32 and 60 with no remainder.

lcm of 32 and 60

How to Find LCM of 32 and 60?

LCM of 32 and 60 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 32 and 60 Using Prime Factorisation Method

The prime factorisation of 32 and 60, respectively, is given by:

32 = (2 × 2 × 2 × 2 × 2) = 25 and

60 = (2 × 2 × 3 × 5) = 22 × 31 × 51

LCM (32, 60) = 480

LCM of 32 and 60 Using Division Method

We’ll divide the numbers (32, 60) by their prime factors to get the LCM of 32 and 60 using the division method (preferably common). The LCM of 32 and 60 is calculated by multiplying these divisors.

2 32 60
2 16 30
2 8 15
2 4 15
2 2 15
3 1 15
5 1 5
x 1 1

No further division can be done.

Hence, LCM (32, 60) = 480

LCM of 32 and 60 Using Listing the Multiples

To calculate the LCM of 32 and 60 by listing out the common multiples, list the multiples as shown below.

Multiples of 32 Multiples of 60
32 60
64 120
96 180
128 240
160 300
…… 360
……… 420
480 480

The smallest common multiple of 32 and 60 is 480.

Therefore LCM (32, 60) = 480

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Video Lesson on Applications of LCM

LCM of 32 and 60 Solved Example

Question: The product of two numbers is 1920. If their GCD is 4, what is their LCM?

Solution:

Given: GCD = 4

product of numbers = 1920

∵ LCM × GCD = product of numbers

⇒ LCM = Product/GCD = 1920/4

Therefore, the LCM is 480.

The probable combination for the given case is LCM(32, 60) = 480.

Frequently Asked Questions on LCM of 32 and 60

Q1

What is the LCM of 32 and 60?

The LCM of 32 and 60 is 480. To find the least common multiple (LCM) of 32 and 60, we need to find the multiples of 32 and 60 (multiples of 32 = 32, 64, 96, 128 . . . . 480; multiples of 60 = 60, 120, 180, 240 . . . . 480) and choose the smallest multiple that is exactly divisible by 32 and 60, i.e., 480.
Q2

List the methods used to find the LCM of 32 and 60.

The methods used to find the LCM of 32 and 60 are Prime Factorization Method, Division Method and Listing multiples.
Q3

Which of the following is the LCM of 32 and 60? 5, 11, 42, 480

The value of LCM of 32, 60 is the smallest common multiple of 32 and 60. The number satisfying the given condition is 480.
Q4

What is the Least Perfect Square Divisible by 32 and 60?

The least number divisible by 32 and 60 = LCM(32, 60)
LCM of 32 and 60 = 2 × 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 32 and 60 = LCM(32, 60) × 2 × 3 × 5 = 14400 [Square root of 14400 = √14400 = ±120] Therefore, 14400 is the required number.
Q5

What is the Relation Between GCF and LCM of 32, 60?

The following equation can be used to express the relation between GCF and LCM of 32 and 60, i.e. GCF × LCM = 32 × 60.

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