When we talk about the Least Common Multiple (LCM) of 50 and 100, we're referring to the smallest number that both 50 and 100 can divide into evenly. In this case, that number is 100. The LCM is sometimes referred to as the Least Common Divisor (LCD), but regardless of what you call it, it's a fundamental concept in mathematics that's important to understand. You can learn more about the concept of LCM and see examples by clicking here.
LCM of 50 and 100 - Methods, Examples, and FAQs
Last Updated on May 31, 2024
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Understanding the LCM of 50 and 100
In simple terms, the Lowest Common Multiple or Least Common Multiple of 50 and 100 is 100.
Methods to Calculate the LCM of 50 and 100
There are several ways to determine the LCM of 50 and 100, including:
- Prime Factorisation
- Division method
- Listing the multiples
Calculating the LCM of 50 and 100 with Prime Factorisation
The Prime Factorisation method involves breaking down the numbers 50 and 100 into their prime factors, and then finding the product of these factors.
50 = 2 × 5 × 5
100 = 2 × 2 × 5 × 5
LCM (50, 100) = 2 × 2 × 5 × 5 = 100
Calculating the LCM of 50 and 100 with the Division Method
The Division Method involves dividing the numbers 50 and 100 by smaller prime numbers, starting with 2, until the remainder is 1.
|
2 |
50 |
100 |
|
2 |
25 |
50 |
|
5 |
25 |
25 |
|
5 |
5 |
5 |
|
× |
1 |
1 |
Therefore, LCM (50, 100) = 2 × 2 × 5 × 5 = 100
Calculating the LCM of 50 and 100 by Listing Multiples
Another way to find the LCM of 50 and 100 is by listing all the multiples of 50 and 100 and finding the smallest common multiple.
|
Multiples of 50 |
Multiples of 100 |
|
50 |
100 |
|
100 |
200 |
|
150 |
300 |
LCM (50, 100) = 100
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Frequently Asked Questions
What is the LCM of 50 and 100?
The LCM of 50 and 100 is 100.
Is the LCM of 50 and 100 the same as the Highest Common Factor of 50 and 100?
No. LCM of 50 and 100 is 100 and the Highest Common Factor of 50 and 100 is 50.
What is the common factor of 50 and 100?
1, 2, 5, 10, 25 and 50 are the common factors of 50 and 100.
What are the first 3 common multiples of 50 and 100?
The first three common multiples of 50 and 100 are 100, 200, and 300.
Is the LCM of 5 and 50 same as the LCM of 5 and 100?
No. LCM of 5 and 50 is 50, whereas the LCM of 5 and 100 is 100. They are not the same.
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