LCM of 315, 510, 422, 219
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 315, 510, 422, 219 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 315, 510, 422, 219. So, keep reading to learn more.
Given numbers are 315,510,422,219
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 315,510,422,219 is 164966130.
Find LCM of 315,510,422,219 with Prime Factorization
| 2 | 315, 510, 422, 219 |
| 3 | 315, 255, 211, 219 |
| 5 | 105, 85, 211, 73 |
| 21, 17, 211, 73 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 21 x 17 x 211 x 73 = 164966130
Therefore, the lowest common multiple of 315,510,422,219 is 164966130.
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.
315 x 510 x 422 x 219 = 14846951700
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.
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
422 : 1, 2, 211, 422
219 : 1, 3, 73, 219
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 315,510,422,219, is 1.
Now, the common factors can be found like this.
315:3x 3x 5x 7
510:2x 3x 5x 17
422:2x 211
219:3x 73
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 5 = 90
Therefore, the value for common factors is 90.
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 = 14846951700/(1x90)
LCM = 14846951700/90
LCM = 164966130
Thus, we can understand that the LCM of 315,510,422,219 is 164966130.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 315, 510, 422, 219
1. What is the LCM of 315, 510, 422, 219?
Answer: LCM of 315, 510, 422, 219 is 164966130.
2. How to calculate the LCM of 315, 510, 422, 219?
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 315, 510, 422, 219.
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}.