LCM of 822, 400, 214, 975
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 822, 400, 214, 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 822, 400, 214, 975. So, keep reading to learn more.
Given numbers are 822,400,214,975
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 822,400,214,975 is 228680400.
Find LCM of 822,400,214,975 with Prime Factorization
| 2 | 822, 400, 214, 975 |
| 3 | 411, 200, 107, 975 |
| 5 | 137, 200, 107, 325 |
| 5 | 137, 40, 107, 65 |
| 137, 8, 107, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 5 x 137 x 8 x 107 x 13 = 228680400
Therefore, the lowest common multiple of 822,400,214,975 is 228680400.
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.
822 x 400 x 214 x 975 = 68604120000
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.
822 : 1, 2, 3, 6, 137, 274, 411, 822
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
214 : 1, 2, 107, 214
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 822,400,214,975, is 1.
Now, the common factors can be found like this.
822:2x 3x 137
400:2x 2x 2x 2x 5x 5
214:2x 107
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 2x 3x 5x 5 = 300
Therefore, the value for common factors is 300.
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 = 68604120000/(1x300)
LCM = 68604120000/300
LCM = 228680400
Thus, we can understand that the LCM of 822,400,214,975 is 228680400.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 822, 400, 214, 975
1. What is the LCM of 822, 400, 214, 975?
Answer: LCM of 822, 400, 214, 975 is 228680400.
2. How to calculate the LCM of 822, 400, 214, 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 822, 400, 214, 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}.