LCM of 12, 18 and 20 is 180. LCM represents the smallest positive number which is a multiple of two or more numbers. The article Least Common Multiple (LCM) will provide you with all the essential information regarding the LCM concept. Students having trouble solving the problems relying on the LCM concept can make use of this article for better guidance. Here, let us learn how to determine the least common multiple of 12, 18 and 20 with the help of solved examples and FAQs.
What is LCM of 12, 18 and 20?
The answer to this question is 180.
How to Find LCM of 12, 18 and 20?
LCM of 12, 18 and 20 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 12, 18 and 20 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 12, 18 and 20 can be represented as;
12 = 2 × 2 × 3
18 = 2 × 3 × 3
20 = 2 × 2 × 5
LCM (12, 18, 20) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12, 18 and 20 Using Division Method
In this method, we divide the numbers 12, 18 and 20 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 12, 18 and 20.
| 2 | 12 | 18 | 20 |
| 2 | 6 | 9 | 10 |
| 3 | 3 | 9 | 5 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (12, 18, 20) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12, 18 and 20 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. Let us glance at the multiples of 12, 18 and 20 provided below
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………, 156, 168, 180,…….
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, ……….
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, …………
LCM (12, 18, 20) = 180
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: Find the smallest number that is divisible by 12, 18, 20 exactly.
Solution: The lowest common multiple of 12, 18 and 20 will be the smallest number that is divisible by 12, 18, 20 exactly. The LCM of 12, 18 and 20 is 180. Therefore the smallest number that is divisible by 12, 18, 20 exactly is 180.
Frequently Asked Questions on LCM of 12, 18 and 20
What is the LCM of 12, 18 and 20?
Is the LCM of 12, 18 and 20 and the HCF of 12, 18 and 20 are same?
180 is the LCM of 12, 18 and 20. True or False.
What are the methods used to find the LCM of 12, 18 and 20?
The methods used to find the LCM of 12, 18 and 20 are
Prime Factorisation
Division Method
Listing the Multiples
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