LCM of 9 and 20 is 180. Students can understand the steps to get the least common multiple of 9 and 20 from the common multiples. (9, 18, 27, 36, 45, ….) and (20, 40, 60, 80, 100, 120, 140,….) are the multiples of 9 and 20. The methods to find the LCM of two numbers are prime factorisation, division and by listing the multiples. The explanation provided improves the conceptual knowledge of students.
Also read: Least common multiple
What is LCM of 9 and 20?
The answer to this question is 180. The LCM of 9 and 20 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 20, is the smallest positive integer 180 which is divisible by both 9 and 20 with no remainder.
How to Find LCM of 9 and 20?
LCM of 9 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 20 Using Prime Factorisation Method
The prime factorisation of 9 and 20, respectively, is given by:
9 = 3 × 3 = 3²
20 = 2 × 2 × 5 = 2²× 5¹
LCM (9, 20) = 180
LCM of 9 and 20 Using Division Method
We’ll divide the numbers (9, 20) by their prime factors to get the LCM of 9 and 20 using the division method (preferably common). The LCM of 9 and 20 is calculated by multiplying these divisors.
|
2 |
9 |
20 |
|
2 |
9 |
10 |
|
3 |
9 |
5 |
|
3 |
3 |
5 |
|
5 |
1 |
5 |
|
× |
1 |
1 |
No further division can be done.
Hence, LCM (9, 20) = 180
LCM of 9 and 20 Using Listing the Multiples
To calculate the LCM of 9 and 20 by listing out the common multiples, list the multiples as shown below
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 162, 171, 180, . . . .
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, . . . ., 120, 140, 160, 180, . . . .
The smallest common multiple of 9 and 20 is 180.
Therefore LCM (9, 20) = 180
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 9 and 20 Solved Examples
Question: Determine the LCM if the product of two numbers is 180 and the GCD is 1.
Solution:
It is given that,
Product of two numbers = 180
GCD = 1
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 180/1
LCM = 180
Hence, the LCM is 180.
Frequently Asked Questions on LCM of 9 and 20
How to find the LCM of 9 and 20?
Write the methods used to get the LCM of 9 and 20.
If the LCM of 9 and 20 is 180, find the GCF.
LCM × GCF = 9 × 20
Given
LCM of 9 and 20 = 180
180 × GCF = 180
GCF = 180/180 = 1
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