LCM of 289, 420, 765, 830
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 289, 420, 765, 830 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 289, 420, 765, 830. So, keep reading to learn more.
Given numbers are 289,420,765,830
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 289,420,765,830 is 30223620.
Find LCM of 289,420,765,830 with Prime Factorization
| 2 | 289, 420, 765, 830 |
| 3 | 289, 210, 765, 415 |
| 5 | 289, 70, 255, 415 |
| 17 | 289, 14, 51, 83 |
| 17, 14, 3, 83 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 17 x 17 x 14 x 3 x 83 = 30223620
Therefore, the lowest common multiple of 289,420,765,830 is 30223620.
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.
289 x 420 x 765 x 830 = 77070231000
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.
289 : 1, 17, 289
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
765 : 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
830 : 1, 2, 5, 10, 83, 166, 415, 830
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 289,420,765,830, is 1.
Now, the common factors can be found like this.
289:17x 17
420:2x 2x 3x 5x 7
765:3x 3x 5x 17
830:2x 5x 83
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 5x 5x 17 = 2550
Therefore, the value for common factors is 2550.
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 = 77070231000/(1x2550)
LCM = 77070231000/2550
LCM = 30223620
Thus, we can understand that the LCM of 289,420,765,830 is 30223620.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 289, 420, 765, 830
1. What is the LCM of 289, 420, 765, 830?
Answer: LCM of 289, 420, 765, 830 is 30223620.
2. How to calculate the LCM of 289, 420, 765, 830?
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 289, 420, 765, 830.
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}.