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LCM of 8 and 18

LCM of 8 and 18 is 72. In Mathematics, the LCM of two numbers is the value that is evenly divisible by the two given numbers. Least common multiple of 8 and 18 is the smallest number we obtain from the common multiples. (8, 16, 24, 32, 40, ….) and (18, 36, 54, 72, 90,….) are the multiples of 8 and 18. We can get the LCM easily using various methods like prime factorisation, division and listing the multiples.

Also read: Least common multiple

What is LCM of 8 and 18?

The answer to this question is 72. The LCM of 8 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 18, is the smallest positive integer 72 which is divisible by both 8 and 18 with no remainder.

lcm of 8 and 18

How to Find LCM of 8 and 18?

LCM of 8 and 18 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 8 and 18 Using Prime Factorisation Method

The prime factorisation of 8 and 18, respectively, is given by:

8 = 2 x 2 x 2 = 2³ 

18 = 2 x 3 x 3 = 2¹ x 3²

LCM (8, 18) = 72

LCM of 8 and 18 Using Division Method

We’ll divide the numbers (8, 18) by their prime factors to get the LCM of 8 and 18 using the division method (preferably common). The LCM of 8 and 18 is calculated by multiplying these divisors.

2 8 18
2 4 9
2 2 9
3 1 9
3 1 3
x 1 1

No further division can be done. 

Hence, LCM (8, 18) = 72

LCM of 8 and 18 Using Listing the Multiples

To calculate the LCM of 8 and 18 by listing out the common multiples, list the multiples as shown below

Multiples of 8 Multiples of 18
8 18
16 36
24 54
32 72
40 90
48 108
56 126
64 144
72 162
80 180

The smallest common multiple of 8 and 18 is 72.

Therefore LCM (8, 18) = 72

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Video Lesson on Applications of LCM

LCM of 8 and 18 Solved Examples 

Question: What is the LCM if the product of two numbers is 144 and the GCD is 2?

Solution:

It is given that

Product of two numbers = 144

GCD = 2

We know that

LCM x GCD = Product of two numbers

LCM = Product/GCD

LCM = 144/2

LCM = 72

Hence, the LCM is 72.

Frequently Asked Questions on LCM of 8 and 18

What is the LCM of 8 and 18?

The LCM of 8 and 18 is 72. To determine the LCM, we should know the multiples of 8 and 18 and the smallest multiple exactly divisible by 8 and 18 has to be found.

Mention the methods used to determine the LCM of 8 and 18.

The methods used to determine the LCM of 8 and 18 are Prime Factorization Method, Division Method and Listing multiples.

Calculate the GCF if the LCM of 8 and 18 is 72.

LCM x GCF = 8 x 18

Given

LCM of 8 and 18 = 72

72 x GCF = 144

GCF = 144/72 = 2

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