LCM of 398, 400, 280, 288
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 398, 400, 280, 288 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 398, 400, 280, 288. So, keep reading to learn more.
Given numbers are 398,400,280,288
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 398,400,280,288 is 10029600.
Find LCM of 398,400,280,288 with Prime Factorization
| 2 | 398, 400, 280, 288 |
| 2 | 199, 200, 140, 144 |
| 2 | 199, 100, 70, 72 |
| 2 | 199, 50, 35, 36 |
| 5 | 199, 25, 35, 18 |
| 199, 5, 7, 18 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 5 x 199 x 5 x 7 x 18 = 10029600
Therefore, the lowest common multiple of 398,400,280,288 is 10029600.
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.
398 x 400 x 280 x 288 = 12837888000
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.
398 : 1, 2, 199, 398
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
280 : 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 398,400,280,288, is 2.
Now, the common factors can be found like this.
398:2x 199
400:2x 2x 2x 2x 5x 5
280:2x 2x 2x 5x 7
288:2x 2x 2x 2x 2x 3x 3
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 2x 5 = 640
Therefore, the value for common factors is 640.
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 = 12837888000/(2x640)
LCM = 12837888000/1280
LCM = 10029600
Thus, we can understand that the LCM of 398,400,280,288 is 10029600.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 398, 400, 280, 288
1. What is the LCM of 398, 400, 280, 288?
Answer: LCM of 398, 400, 280, 288 is 10029600.
2. How to calculate the LCM of 398, 400, 280, 288?
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 398, 400, 280, 288.
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}.