LCM of 200 and 300 is 600. The Least Common multiple(LCM) or Lowest Common Multiple(LCM) is the least number that is divisible by a given set of numbers. In the given set of numbers 200 and 300, 600 is the first(least or smallest) number that is common in the set of multiples of 200 and 300. 1200 is also the common multiple of 200 and 300. However, 600 is the smallest. Hence 600 is the LCM which is also known as LCD, Least Common Divisor for 200 and 300. You can read more on LCM for further details.
What is the LCM of 200 and 300?
The Least Common Multiple or Lowest Common Multiple of 200 and 300 is 600.
How to Find LCM of 200 and 300?
LCM of 200 and 300 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 200 and 300 Using Prime Factorisation Method
In the Prime Factorisation method, 200 and 300 can be expressed as;
200 = 2 × 2 × 2 × 5 × 5
300 = 2 × 2 × 3 × 5 × 5
Among the common factors of 200 and 300, the factors 2, 2, 5, 5 are common. These are multiplied with 2 and 3 that are not common. Thus LCM is obtained.
LCM (200, 300) = 2 × 2 × 2 × 3 × 5 × 5 = 600
LCM of 200 and 300 Using Division Method
In the Division Method, the numbers 200 and 300 are multiplied by prime factors and the product of these prime divisors forms the LCM.
|
2 |
200 |
300 |
|
2 |
100 |
150 |
|
2 |
50 |
75 |
|
3 |
25 |
75 |
|
5 |
25 |
25 |
|
5 |
5 |
5 |
|
× |
1 |
1 |
LCM (200, 300) = 2 × 2 × 2 × 3 × 5 × 5 = 600
LCM of 200 and 300 Using Listing the Multiples
By listing all the multiples of 200 and 300, we can observe the first common multiple, which is the LCM. Below is the list of multiples for 200 and 300
|
Multiples of 200 |
Multiples of 300 |
|
200 |
300 |
|
400 |
600 |
|
600 |
900 |
|
800 |
1200 |
LCM (200, 300) = 600
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 200 and 300?
Answer: 600 is the smallest number that is divisible by both 200 and 300.
What is the LCM for 100, 200 and 300?
Answer: LCM for 100, 200 and 300 is 600 as 100 is a multiple of 200 and 300.
Comments