LCM of 9 and 45 is 45. Students can learn how to obtain the least common multiple of 9 and 45 from the common multiples. (9, 18, 27, 36, 45, 54, ….) and (45, 90, 135, 180,….) are the multiples of 19 and 45. The process which can be used to find the LCM of two numbers is prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 9 and 45?
The answer to this question is 45. The LCM of 9 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 45, is the smallest positive integer 45 which is divisible by both 9 and 45 with no remainder.
How to Find LCM of 9 and 45?
LCM of 9 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 45 Using Prime Factorisation Method
The prime factorisation of 9 and 45, respectively, is given by:
9 = 3 x 3 = 3²
45 = 3 x 3 x 5 = 3² x 5¹
LCM (9, 45) = 45
LCM of 9 and 45 Using Division Method
We’ll divide the numbers (9, 45) by their prime factors to get the LCM of 9 and 45 using the division method (preferably common). The LCM of 9 and 45 is calculated by multiplying these divisors.
3 | 9 | 45 |
3 | 3 | 15 |
5 | 1 | 5 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 45) = 45
LCM of 9 and 45 Using Listing the Multiples
To calculate the LCM of 9 and 45 by listing out the common multiples, list the multiples as shown below:
Multiples of 9 | Multiples of 45 |
9 | 45 |
18 | 90 |
27 | 135 |
36 | 180 |
45 | 225 |
54 | 270 |
LCM (9, 45) = 45
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Video Lesson on Applications of LCM
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LCM of 9 and 45 Solved Example
Question: What is the smallest number divisible by 9 and 45 exactly?
Solution:
We know that
The smallest number exactly divisible by 9 and 45 is the LCM.
Multiples of 9 = 9, 18, 27, 36, 45, 54,…..
Multiples of 45 = 45, 90, 135, 180, ….
Hence, the LCM of 9 and 45 is 45.
Frequently Asked Questions on LCM of 9 and 45
In the numbers 45, 30, 28, 18, what is the LCM of 9 and 45?
Find the GCF if the LCM of 9 and 45 is 45.
LCM x GCF = 9 x 45
Given
LCM of 9 and 45 = 45
45 x GCF = 405
GCF = 405/45 = 9
What is the relation between GCF and LCM of 9 and 45?
The relation between GCF and LCM of 9 and 45 is
LCM x GCF = 9 x 45
LCM x GCF = 405
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