LCM of 509, 414, 693, 784
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 509, 414, 693, 784 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 509, 414, 693, 784. So, keep reading to learn more.
Given numbers are 509,414,693,784
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 509,414,693,784 is 908650512.
Find LCM of 509,414,693,784 with Prime Factorization
| 2 | 509, 414, 693, 784 |
| 3 | 509, 207, 693, 392 |
| 3 | 509, 69, 231, 392 |
| 7 | 509, 23, 77, 392 |
| 509, 23, 11, 56 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 7 x 509 x 23 x 11 x 56 = 908650512
Therefore, the lowest common multiple of 509,414,693,784 is 908650512.
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.
509 x 414 x 693 x 784 = 114489964512
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.
509 : 1, 509
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
693 : 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 509,414,693,784, is 1.
Now, the common factors can be found like this.
509:509
414:2x 3x 3x 23
693:3x 3x 7x 11
784:2x 2x 2x 2x 7x 7
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 7 = 126
Therefore, the value for common factors is 126.
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 = 114489964512/(1x126)
LCM = 114489964512/126
LCM = 908650512
Thus, we can understand that the LCM of 509,414,693,784 is 908650512.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 509, 414, 693, 784
1. What is the LCM of 509, 414, 693, 784?
Answer: LCM of 509, 414, 693, 784 is 908650512.
2. How to calculate the LCM of 509, 414, 693, 784?
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 509, 414, 693, 784.
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}.