LCM of 20 and 45 is 180.The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 20 and 45, 180 is the first (least or smallest) number that is common in the set of multiples of 20 and 45. The LCM is also known as LCD, Least Common Divisor. You can use LCM for more details.
What is LCM of 20 and 45
The Least Common Multiple or Lowest Common Multiple of 20 and 45 is 180.
How to Find LCM of 20 and 45?
LCM of 20 and 45 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20 and 45 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 20 and 45 can be expressed as;
20 = 2 x 2 x 5
45 = 3 x 3 x 5
LCM (20, 45) = 2 x 2 x 3 x 3 x 5 = 180
LCM of 20 and 45 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
2 |
20 |
45 |
|
2 |
10 |
45 |
|
3 |
5 |
45 |
|
3 |
5 |
15 |
|
5 |
5 |
5 |
|
x |
1 |
1 |
LCM (20, 45) = 2 x 2 x 3 x 3 x 5 = 180
LCM of 20 and 45 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 20 and 45
|
Multiples of 20 |
Multiples of 45 |
|
20 |
45 |
|
40 |
90 |
|
60 |
135 |
|
80 |
180 |
|
100 |
225 |
|
120 |
270 |
|
140 |
315 |
|
160 |
360 |
|
180 |
405 |
|
200 |
450 |
LCM (20, 45) = 180
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 20 and 45?
Answer: 180 is the smallest number that is divisible by both 20 and 45.
What is the LCM for 3, 9, 20 and 45?
Answer: LCM for 3, 9, 20 and 45 is 180.
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