LCM of 30 and 75 is 150.The Least Common Divisor, or 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 30 and 75, 150 is the first(least or smallest) number that is common in the set of multiples of 30 and 75. You can use the LCM with Examples for more details.
What is LCM of 30 and 75
The Least Common Multiple or Lowest Common Multiple of 30 and 75 is 150.
How to Find LCM of 30 and 75?
LCM of 30 and 75 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 75 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 30 and 75 can be expressed as;
30 = 2 × 3 × 5
75 = 3 × 5 × 5
LCM (30, 75) = 2 × 3 × 5 × 5 = 150
LCM of 30 and 75 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 |
75 |
|
3 |
15 |
75 |
|
5 |
5 |
25 |
|
5 |
1 |
5 |
|
× |
1 |
1 |
LCM (30, 75) = 2 × 3 × 5 × 5 = 150
LCM of 30 and 75 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 75
|
Multiples of 30 |
Multiples of 75 |
|
30 |
75 |
|
60 |
150 |
|
90 |
225 |
|
120 |
300 |
|
150 |
375 |
|
180 |
450 |
LCM (30, 75) = 150
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 30 and 75?
Answer: 150 is the smallest number that is divisible by both 30 and 75.
What is the LCM for 10, 25, 30 and 75?
Answer: LCM for 10, 25, 30 and 75 is 150.
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