LCM of 200, 408, 146, 400
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 200, 408, 146, 400 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 200, 408, 146, 400. So, keep reading to learn more.
Given numbers are 200,408,146,400
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 200,408,146,400 is 1489200.
Find LCM of 200,408,146,400 with Prime Factorization
| 2 | 200, 408, 146, 400 |
| 2 | 100, 204, 73, 200 |
| 2 | 50, 102, 73, 100 |
| 5 | 25, 51, 73, 50 |
| 5 | 5, 51, 73, 10 |
| 1, 51, 73, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 5 x 5 x 1 x 51 x 73 x 2 = 1489200
Therefore, the lowest common multiple of 200,408,146,400 is 1489200.
LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
Firstly, we have to find the product of all the numbers.
200 x 408 x 146 x 400 = 4765440000
Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
146 : 1, 2, 73, 146
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 200,408,146,400, is 2.
Now, the common factors can be found like this.
200:2x 2x 2x 5x 5
408:2x 2x 2x 3x 17
146:2x 73
400:2x 2x 2x 2x 5x 5
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 2x 2x 2x 2x 2x 5x 5 = 1600
Therefore, the value for common factors is 1600.
Now that we have all the elements of the formula, we can plug them in to calculate the LCM.
LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
LCM = 4765440000/(2x1600)
LCM = 4765440000/3200
LCM = 1489200
Thus, we can understand that the LCM of 200,408,146,400 is 1489200.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 200, 408, 146, 400
1. What is the LCM of 200, 408, 146, 400?
Answer: LCM of 200, 408, 146, 400 is 1489200.
2. How to calculate the LCM of 200, 408, 146, 400?
The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 200, 408, 146, 400.
3. What is the LCM formula?
The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.