LCM of 8, 12 and 18 is 72. LCM represents the smallest positive number which is a multiple of two or more numbers. The article Prime Factorisation and Division Method for LCM and HCF help students to enhance their problem-solving skills, which is crucial from an exam point of view. Students solve problems based on the LCM concept effortlessly by going through the article designed by the experts on a daily basis. Let us grasp the simple format to find the least common multiple of 8, 12 and 18 in this article.
What is LCM of 8, 12 and 18?
The answer to this question is 72.
How to Find LCM of 8, 12 and 18?
LCM of 8, 12 and 18 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 8, 12 and 18 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 8, 12 and 18 can be expressed as;
8 = 2 × 2 × 2
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM (8, 12, 18) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 8, 12 and 18 Using Division Method
In this method, we divide the numbers 8, 12 and 18 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 8, 12 and 18.
| 2 | 8 | 12 | 18 |
| 2 | 4 | 6 | 9 |
| 2 | 2 | 3 | 9 |
| 3 | 1 | 3 | 9 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (8, 12, 18) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 8, 12 and 18 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below list gives the multiples of 8, 12 and 18:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72,……….
Multiples of 12: 12, 24, 36, 48, 60, 72, ……………
Multiples of 18: 18, 36, 54, 72, ………….
LCM (8, 12, 18) = 72
Related Articles
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 8, 12, 18 exactly?
Solution: The smallest number that is divisible by 8, 12, 18 exactly is their LCM
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72,……….
Multiples of 12: 12, 24, 36, 48, 60, 72, ……………
Multiples of 18: 18, 36, 54, 72, ………….
Hence 72 is the smallest number that is divisible by 8, 12, 18 exactly.
Frequently Asked Questions on LCM of 8, 12 and 18
What is the LCM of 8, 12 and 18?
Write the LCM of 8, 12 and 18 and the HCF of 8, 12 and 18.
92 is the LCM of 8, 12 and 18. True or False.
Mention the methods to find the LCM of 8, 12 and 18.
The following methods are used to find the LCM of 8, 12 and 18
Prime Factorisation
Division Method
Listing the Multiples
Using the prime factorisation, find the LCM of 8, 12 and 18.
To find the LCM using prime factorisation, we express the numbers as the product of prime factors
8 = 2 × 2 × 2
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM (8, 12, 18) = 2 × 2 × 2 × 3 × 3 = 72
Comments