LCM of 305, 214, 810, 324
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 305, 214, 810, 324 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 305, 214, 810, 324. So, keep reading to learn more.
Given numbers are 305,214,810,324
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 305,214,810,324 is 10573740.
Find LCM of 305,214,810,324 with Prime Factorization
| 2 | 305, 214, 810, 324 |
| 3 | 305, 107, 405, 162 |
| 3 | 305, 107, 135, 54 |
| 3 | 305, 107, 45, 18 |
| 3 | 305, 107, 15, 6 |
| 5 | 305, 107, 5, 2 |
| 61, 107, 1, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 3 x 3 x 5 x 61 x 107 x 1 x 2 = 10573740
Therefore, the lowest common multiple of 305,214,810,324 is 10573740.
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.
305 x 214 x 810 x 324 = 17129458800
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.
305 : 1, 5, 61, 305
214 : 1, 2, 107, 214
810 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
324 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 305,214,810,324, is 1.
Now, the common factors can be found like this.
305:5x 61
214:2x 107
810:2x 3x 3x 3x 3x 5
324:2x 2x 3x 3x 3x 3
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 3x 3x 3x 5 = 1620
Therefore, the value for common factors is 1620.
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 = 17129458800/(1x1620)
LCM = 17129458800/1620
LCM = 10573740
Thus, we can understand that the LCM of 305,214,810,324 is 10573740.
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FAQs on LCM of 305, 214, 810, 324
1. What is the LCM of 305, 214, 810, 324?
Answer: LCM of 305, 214, 810, 324 is 10573740.
2. How to calculate the LCM of 305, 214, 810, 324?
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 305, 214, 810, 324.
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}.