LCM of 30 and 60 is 60. Consider the common multiples of 30 and 60, i.e 60, 120,180, 240…The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer. In this case, 60 is the smallest/least or first common multiple. Hence 60 is the LCM which is also known as LCD, Least Common Divisor for 30 and 60. You can read more on LCM for further details.
What is LCM of 30 and 60
The Least Common Multiple or Lowest Common Multiple of 30 and 60 is 60.
How to Find LCM of 30 and 60?
LCM of 30 and 60 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 60 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 30 and 60 can be expressed as;
30 = 2 x 3 x 5
60 = 2 x 2 x 3 x 5
LCM (30, 60) = 2 x 2 x 3 x 5 = 60
LCM of 30 and 60 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 |
30 |
60 |
|
3 |
15 |
30 |
|
5 |
5 |
10 |
|
2 |
1 |
2 |
|
x |
1 |
1 |
Hence LCM (30, 60) = 2 x 2 x 3 x 5 = 60
LCM of 30 and 60 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 30 and 60
|
Multiples of 30 |
Multiples of 60 |
|
30 |
60 |
|
60 |
120 |
|
90 |
180 |
|
120 |
240 |
|
150 |
300 |
LCM (30, 60) = 60
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 30 and 60?
Answer: 60 is the smallest number that is divisible by both 30 and 60.
What is the LCM for 10, 30 and 60?
Answer: LCM for 10, 30 and 60 is 60.
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