LCM of 300, 214, 390, 344, 280
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 300, 214, 390, 344, 280 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 300, 214, 390, 344, 280. So, keep reading to learn more.
Given numbers are 300,214,390,344,280
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 300,214,390,344,280 is 251214600.
Find LCM of 300,214,390,344,280 with Prime Factorization
| 2 | 300, 214, 390, 344, 280 |
| 2 | 150, 107, 195, 172, 140 |
| 2 | 75, 107, 195, 86, 70 |
| 3 | 75, 107, 195, 43, 35 |
| 5 | 25, 107, 65, 43, 35 |
| 5, 107, 13, 43, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 5 x 107 x 13 x 43 x 7 = 251214600
Therefore, the lowest common multiple of 300,214,390,344,280 is 251214600.
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.
300 x 214 x 390 x 344 x 280 = 2411660160000
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.
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
214 : 1, 2, 107, 214
390 : 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
344 : 1, 2, 4, 8, 43, 86, 172, 344
280 : 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 300,214,390,344,280, is 2.
Now, the common factors can be found like this.
300:2x 2x 3x 5x 5
214:2x 107
390:2x 3x 5x 13
344:2x 2x 2x 43
280:2x 2x 2x 5x 7
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 3x 5x 5 = 4800
Therefore, the value for common factors is 4800.
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 = 2411660160000/(2x4800)
LCM = 2411660160000/9600
LCM = 251214600
Thus, we can understand that the LCM of 300,214,390,344,280 is 251214600.
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FAQs on LCM of 300, 214, 390, 344, 280
1. What is the LCM of 300, 214, 390, 344, 280?
Answer: LCM of 300, 214, 390, 344, 280 is 251214600.
2. How to calculate the LCM of 300, 214, 390, 344, 280?
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 300, 214, 390, 344, 280.
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}.