LCM of 12, 18 and 24

LCM of 12, 18 and 24 is 72. The least common multiple is a method to find the smallest common multiple between any two or more numbers. Students can make use of the article Least Common Multiple (LCM) formulated by experts for effective exam preparation. This article is well structured in a simple language to make the learning of the LCM concept an easy task. Let us learn how to calculate the least common multiple of 12, 18 and 24 along with examples and FAQs in this article.

What is LCM of 12, 18 and 24?

The answer to this question is 72.

lcm of 12 18 and 24

How to Find LCM of 12, 18 and 24?

LCM of 12, 18 and 24 can be obtained using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 12, 18 and 24 Using Prime Factorisation Method

By prime factorisation method, we can write 12, 18 and 24 as the product of prime numbers, such that;

12 = 2 × 2 × 3

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

LCM (12, 18, 24) = 2 × 2 × 2 × 3 × 3 = 72

LCM of 12, 18 and 24 Using Division Method

In this method, we divide the numbers 12, 18 and 24 by their prime factors until we get the result as one in the complete row to find their LCM. The product of these divisors denotes the least common multiple of 12, 18 and 24. This can be shown as below.

2 12 18 24
2 6 9 12
2 3 9 6
3 3 9 3
3 1 3 1
x 1 1 1

No more further division can be done.

Therefore, LCM (12, 18, 24) = 2 × 2 × 2 × 3 × 3 = 72

LCM of 12, 18 and 24 Using Listing the Multiples

Here we list out the multiples of 12, 18 and 24 to calculate their least common multiple as shown below:

Multiples of 12 Multiples of 18 Multiples of 24
12 18 24
24 36 48
36 54 72
48 72 96
60 90 120
72 108 144
84 126 168

LCM (12, 18, 24) = 72

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Prime Factorization and Division Method for LCM and HCF

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Video Lesson on Applications of LCM

Solved Example

Question: What is the smallest number that is divisible by 12, 18, 24 exactly?

Solution: The smallest number that is divisible by 12, 18, 24 exactly is their LCM. We know that the LCM of 12, 18 and 24 is 72. Thus the smallest number that is divisible by 12, 18, 24 exactly is 72. 

Frequently Asked Questions on LCM of 12, 18 and 24

Q1

What is the LCM of 12, 18 and 24?

The LCM of 12, 18 and 24 is 72.
Q2

Is the LCM of 12, 18 and 24 the same as the HCF of 12,18 and 24?

No. The LCM of 12, 18 and 24 is 72 and the HCF of 12, 18 and 24 is 6.
Q3

92 is the LCM of 12, 18 and 24. True or False.

False. The LCM of 12, 18 and 24 is 72.
Q4

List the methods used to determine the LCM of 12, 18 and 24.

The methods used to determine the LCM of 12, 18 and 24 are

Prime Factorisation

Division Method

Listing the Multiples

Q5

Find the LCM of 12, 18 and 24 by Prime Factorisation.

12 = 2 × 2 × 3

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

LCM (12, 18, 24) = 2 × 2 × 2 × 3 × 3 = 72

Hence the LCM of 12, 18 and 24 by Prime Factorisation is 72

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