LCM of 288, 400, 912, 214
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 288, 400, 912, 214 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 288, 400, 912, 214. So, keep reading to learn more.
Given numbers are 288,400,912,214
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 288,400,912,214 is 14637600.
Find LCM of 288,400,912,214 with Prime Factorization
| 2 | 288, 400, 912, 214 |
| 2 | 144, 200, 456, 107 |
| 2 | 72, 100, 228, 107 |
| 2 | 36, 50, 114, 107 |
| 3 | 18, 25, 57, 107 |
| 6, 25, 19, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 6 x 25 x 19 x 107 = 14637600
Therefore, the lowest common multiple of 288,400,912,214 is 14637600.
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.
288 x 400 x 912 x 214 = 22483353600
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.
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
912 : 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912
214 : 1, 2, 107, 214
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 288,400,912,214, is 2.
Now, the common factors can be found like this.
288:2x 2x 2x 2x 2x 3x 3
400:2x 2x 2x 2x 5x 5
912:2x 2x 2x 2x 3x 19
214:2x 107
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 2x 3 = 768
Therefore, the value for common factors is 768.
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 = 22483353600/(2x768)
LCM = 22483353600/1536
LCM = 14637600
Thus, we can understand that the LCM of 288,400,912,214 is 14637600.
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FAQs on LCM of 288, 400, 912, 214
1. What is the LCM of 288, 400, 912, 214?
Answer: LCM of 288, 400, 912, 214 is 14637600.
2. How to calculate the LCM of 288, 400, 912, 214?
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 288, 400, 912, 214.
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}.