LCM of 72 and 108

LCM of 72 and 108 is 216. Among all common multiples of 72 and 108, the LCM of 72 and 108 is the smallest. (72, 144, 216, 288, etc.) and (108, 216, 324, 432, 540, etc.) are the first few multiples of 72 and 108. Prime factorization, listing multiples, and division are the three most frequent methods for determining the LCM of 72 and 108. In mathematics, the LCM of any two numbers is the value that divides the two values equally.

What is LCM of 72 and 108?

The answer to this question is 216. The LCM of 72 and 108 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 72 and 108, is the smallest positive integer 216 which is divisible by both 72 and 108 with no remainder.

lcm of 72 and 108

Also read: Least common multiple

How to Find LCM of 72 and 108?

LCM of 72 and 108 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 72 and 108 Using Prime Factorisation Method

The prime factorisation of 72 and 108, respectively, is given by:

72 = (2 × 2 × 2 × 3 × 3) = 23 × 32 and

108 = (2 × 2 × 3 × 3 × 3) = 22 × 33

LCM (72, 108) = 216

LCM of 72 and 108 Using Division Method

We’ll divide the numbers (72, 108) by their prime factors to get the LCM of 72 and 108 using the division method (preferably common). The LCM of 72 and 108 is calculated by multiplying these divisors.

2 72 108
2 36 54
3 18 27
3 6 9
3 2 3
2 2 1
x 1 1

No further division can be done.

Hence, LCM (72, 108) = 216

LCM of 72 and 108 Using Listing the Multiples

To calculate the LCM of 72 and 108 by listing out the common multiples, list the multiples as shown below:

Multiples of 72 Multiples of 108
72 108
144 216
216 324
288 432
360 540

The smallest common multiple of 72 and 108 is 216.

LCM (72, 108) = 216

Related Articles

Video Lesson on Applications of LCM

LCM of 72 and 108 Solved Example

The GCD and LCM of two numbers are 36 and 216 respectively. If one number is 108, find the other number.

Let the other number be b.

GCD × LCM = 108 × b

b = (GCD × LCM)/108

b = (36 × 216)/108

b = 72

Therefore, the other number is 72.

Frequently Asked Questions on LCM of 72 and 108

Q1

What is the LCM of 72 and 108?

The LCM of 72 and 108 is 216. To find the LCM of 72 and 108, we need to find the multiples of 72 and 108 (multiples of 72 = 72, 144, 216, 288; multiples of 108 = 108, 216, 324, 432) and choose the smallest multiple that is exactly divisible by 72 and 108, i.e., 216.
Q2

List the methods used to find the LCM of 72 and 108.

The methods used to find the LCM of 72 and 108 are the Prime Factorization Method, Division Method and Listing multiples.
Q3

Which of the following is the LCM of 72 and 108? 35, 12, 45, 216

The value of LCM of 72, 108 is the smallest common multiple of 72 and 108. The number satisfying the given condition is 216.

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*