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.
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
Related Articles
Prime Factorization and Division Method for LCM and HCF
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
What is the LCM of 12, 18 and 24?
Is the LCM of 12, 18 and 24 the same as the HCF of 12,18 and 24?
92 is the LCM of 12, 18 and 24. True or False.
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
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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