LCM of 214, 819, 300, 975
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 214, 819, 300, 975 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 214, 819, 300, 975. So, keep reading to learn more.
Given numbers are 214,819,300,975
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 214,819,300,975 is 8763300.
Find LCM of 214,819,300,975 with Prime Factorization
| 2 | 214, 819, 300, 975 |
| 3 | 107, 819, 150, 975 |
| 5 | 107, 273, 50, 325 |
| 5 | 107, 273, 10, 65 |
| 13 | 107, 273, 2, 13 |
| 107, 21, 2, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 5 x 13 x 107 x 21 x 2 x 1 = 8763300
Therefore, the lowest common multiple of 214,819,300,975 is 8763300.
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.
214 x 819 x 300 x 975 = 51265305000
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.
214 : 1, 2, 107, 214
819 : 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
975 : 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 214,819,300,975, is 1.
Now, the common factors can be found like this.
214:2x 107
819:3x 3x 7x 13
300:2x 2x 3x 5x 5
975:3x 5x 5x 13
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 3x 5x 5x 13 = 5850
Therefore, the value for common factors is 5850.
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 = 51265305000/(1x5850)
LCM = 51265305000/5850
LCM = 8763300
Thus, we can understand that the LCM of 214,819,300,975 is 8763300.
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FAQs on LCM of 214, 819, 300, 975
1. What is the LCM of 214, 819, 300, 975?
Answer: LCM of 214, 819, 300, 975 is 8763300.
2. How to calculate the LCM of 214, 819, 300, 975?
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 214, 819, 300, 975.
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}.