LCM of 45 and 60 is 180. The value divisible evenly by 45 and 60 gives the LCM value. Least common multiples of 45 and 60 can be found from the multiples which are common. (45, 90, 135, 180, 225, 270, ….) and (60, 120, 180, 240, 300, 360,….) are the multiples of 45 and 60. Students will learn how LCM of two numbers can be found using prime factorization, division and by listing the multiples using this article as a reference.
Also read: Least common multiple
What is LCM of 45 and 60?
The answer to this question is 180. The LCM of 45 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 45 and 60, is the smallest positive integer 180 which is divisible by both 45 and 60 with no remainder.
How to Find LCM of 45 and 60?
LCM of 45 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 45 and 60 Using Prime Factorisation Method
The prime factorisation of 45 and 60, respectively, is given by:
45 = 3 x 3 x 5 = 3² x 5
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
LCM (45, 60) = 180
LCM of 45 and 60 Using Division Method
We’ll divide the numbers (45, 60) by their prime factors to get the LCM of 45 and 60 using the division method (preferably common). The LCM of 45 and 60 is calculated by multiplying these divisors.
| 2 | 45 | 60 |
| 2 | 45 | 30 |
| 3 | 45 | 15 |
| 3 | 15 | 5 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (45, 60) = 180
LCM of 45 and 60 Using Listing the Multiples
To calculate the LCM of 45 and 60 by listing out the common multiples, list the multiples as shown below
| Multiples of 45 | Multiples of 60 |
| 45 | 60 |
| 90 | 120 |
| 135 | 180 |
| 180 | 240 |
| 225 | – |
| 270 | – |
LCM (45, 60) = 180
Related Articles
Video Lesson on Applications of LCM
LCM of 45 and 60 Solved Example
Which is the smallest number divisible by 45 and 60 exactly?
Solution:
The smallest number divisible by 45 and 60 exactly is the LCM.
Multiples of 45 = 45, 90, 135, 180, 225, ….
Multiples of 60 = 60, 120, 180, 240, 300, …..
Hence, the LCM of 45 and 60 is 180.
Frequently Asked Questions on LCM of 45 and 60
What is the LCM of 45 and 60?
What is the GCF if the LCM of 45 and 60 is 180?
LCM x GCF = 45 x 60
Given
LCM of 45 and 60 = 180
180 x GCF = 2700
GCF = 2700/180 = 15
What is the relation between GCF and LCM of 45 and 60?
The relation between GCF and LCM of 45 and 60 is
LCM x GCF = 45 x 60
LCM x GCF = 2700
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