LCM of 12, 16 and 18 is 144. LCM denotes the smallest positive number that is a multiple of two or more numbers. Experts formulated the article LCM with Examples in simple and understandable language to help students ace the exam. This article provides a detailed explanation for a better hold on the LCM concept. In this article, let us learn the simple method of calculating the least common multiple of 12, 16 and 18 using prime factorisation, division method and a list of multiples.
What is LCM of 12, 16 and 18?
The Least Common Multiple of 12, 16 and 18 is 144.
How to Find LCM of 12, 16 and 18?
The LCM of 12, 16 and 18 can be obtained by using the methods given below:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 12, 16 and 18 Using Prime Factorisation Method
In the prime factorisation method, LCM of 12, 16 and 18 can be obtained by multiplying prime factors raised to their respective highest power.
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
18 = 2 × 3 × 3
LCM (12, 16, 18) = 2 × 2 × 2 × 2 × 3 × 3 = 144
LCM of 12 16 and 18 Using Division Method
In the division method, to calculate the LCM, we divide the numbers 12, 16 and 18 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 12, 16 and 18.
| 2 | 12 | 16 | 18 |
| 2 | 6 | 8 | 9 |
| 2 | 3 | 4 | 9 |
| 2 | 3 | 2 | 9 |
| 3 | 3 | 1 | 9 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (12, 16, 18) = 2 × 2 × 2 × 2 × 3 × 3 = 144
LCM of 12, 16 and 18 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to find the least common multiple among them. Let us have a look at the multiples of 12, 16 and 18 given below.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ………
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ……….
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, …………
LCM (12, 16, 18) = 144
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by 12, 16 and 18 exactly?
Solution: 144 is the smallest number that is divisible by 12, 16 and 18 exactly.
2. What is the lowest common factor of 12, 16 and 18?
Solution: The lowest common factor of 12, 16 and 18 is 144.
Frequently Asked Questions on LCM of 12, 16 and 18
What is the LCM of 12, 16 and 18?
Is the LCM of 12, 16 and 18 the same as the HCF of 12, 16 and 18?
3 is the highest common factor of 12, 16 and 18. True or False.
What are the methods used to find the LCM of 12, 16 and 18?
The methods used to find the LCM of 12, 16 and 18 are
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 12, 16 and 18 using the prime factorisation method.
In this method, to find the LCM, we write the numbers as the product of prime factors
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
18 = 2 × 3 × 3
LCM (12, 16, 18) = 2 × 2 × 2 × 2 × 3 × 3 = 144
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