LCM of 60 and 90 is 180. The Least Common Divisor (LCD) also known as 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 60 and 90, 180 is the first(least or smallest) number that is common in the set of multiples of 60 and 90. You can refer to LCM with Examples for clarity.
What is LCM of 60 and 90
The Least Common Multiple or Lowest Common Multiple of 60 and 90 is 180.
How to Find LCM of 60 and 90?
LCM of 60 and 90 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 90 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 60 and 90 can be expressed as;
60 = 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
LCM (60, 90) = 2 x 2 x 3 x 3 x 5 = 180
LCM of 60 and 90 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 |
60 |
90 |
|
3 |
30 |
45 |
|
5 |
10 |
15 |
|
2 |
2 |
3 |
|
3 |
1 |
3 |
|
x |
1 |
1 |
LCM (60, 90) = 2 x 2 x 3 x 3 x 5 = 180
LCM of 60 and 90 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 60 and 90
|
Multiples of 60 |
Multiples of 90 |
|
60 |
90 |
|
120 |
180 |
|
180 |
270 |
|
240 |
360 |
|
300 |
450 |
LCM (60, 90) = 180
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 60 and 90?
Answer: 180 is the smallest number that is divisible by both 60 and 90.
What is the LCM for 3, 60 and 90?
Answer: LCM for 3, 60 and 90 is 180.
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