LCM of 100 and 200 is 200. By making a note of the multiples of 100 and 200, the number evenly divisible by 100 and 200 is the LCM. Least common multiple of 100 and 200 is the multiple we get commonly using the process of multiplication. (100, 200, 300, 400, 500, 600, 700, ….) and (200, 400, 600, 800, ….) are the multiples of 100 and 200. Students can learn the steps to find the LCM of two numbers using listing multiples, prime factorization and division methods.
Also read: Least common multiple
What is LCM of 100 and 200?
The answer to this question is 200. The LCM of 100 and 200 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 100 and 200, is the smallest positive integer 200 which is divisible by both 100 and 200 with no remainder.
How to Find LCM of 100 and 200?
LCM of 100 and 200 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 100 and 200 Using Prime Factorisation Method
The prime factorisation of 100 and 200, respectively, is given by:
100 = 2 x 2 x 5 x 5 = 2² x 5²
200 = 2 x 2 x 2 x 5 x 5 = 2³ x 5²
LCM (100, 200) = 200
LCM of 100 and 200 Using Division Method
We’ll divide the numbers (100, 200) by their prime factors to get the LCM of 100 and 200 using the division method (preferably common). The LCM of 100 and 200 is calculated by multiplying these divisors.
|
2 |
100 |
200 |
|
2 |
50 |
100 |
|
2 |
25 |
50 |
|
5 |
25 |
25 |
|
5 |
5 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (100, 200) = 200
LCM of 100 and 200 Using Listing the Multiples
To calculate the LCM of 100 and 200 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 100 |
Multiples of 200 |
|
100 |
200 |
|
200 |
400 |
|
300 |
600 |
|
400 |
800 |
|
500 |
1000 |
LCM (100, 200) = 200
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 100 and 200 Solved Examples
Question: Calculate the smallest number exactly divisible by 100 and 200.
Solution:
We know that,
LCM is the smallest number exactly divisible by 100 and 200.
(100, 200, 300, 400, 500, 600, 700, ….) are the multiples of 100
(200, 400, 600, 800, …..) are the multiples of 200
Hence, the LCM of 100 and 200 is 200.
Frequently Asked Questions on LCM of 100 and 200
What are the methods used to determine the LCM of 100 and 200?
Using the prime factorisation method, find the LCM of 100 and 200.
First we have to know the factors to find the LCM
100 = 2 x 2 x 5 x 5
200 = 2 x 2 x 2 x 5 x 5
LCM is the product of prime factors raised to the highest exponent among 100 and 200.
LCM of 100 and 200 = 200
Find the GCF if the LCM of 100 and 200 is 200.
LCM x GCF = 100 x 200
As the LCM = 200
200 x GCF = 20000
GCF = 20000/200 = 100
The LCM and GCD of two numbers are 200 and 100. If one number is 200, calculate the other.
Consider y as the other number
GCD x LCM = 200 x y
y = (GCD x LCM)/200
y = (100 x 200)/ 200
y = 100
Hence, the other number is 100.
Write the relation between GCF and LCM of 100 and 200.
The relation between GCF and LCM of 100 and 200 is
GCF x LCM = 100 x 200
GCF x LCM = 20000
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