LCM of 780, 723, 828, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 780, 723, 828, 414 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 780, 723, 828, 414. So, keep reading to learn more.
Given numbers are 780,723,828,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 780,723,828,414 is 12970620.
Find LCM of 780,723,828,414 with Prime Factorization
| 2 | 780, 723, 828, 414 |
| 2 | 390, 723, 414, 207 |
| 3 | 195, 723, 207, 207 |
| 3 | 65, 241, 69, 69 |
| 23 | 65, 241, 23, 23 |
| 65, 241, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 23 x 65 x 241 x 1 x 1 = 12970620
Therefore, the lowest common multiple of 780,723,828,414 is 12970620.
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.
780 x 723 x 828 x 414 = 193314120480
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.
780 : 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
723 : 1, 3, 241, 723
828 : 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 780,723,828,414, is 3.
Now, the common factors can be found like this.
780:2x 2x 3x 5x 13
723:3x 241
828:2x 2x 3x 3x 23
414:2x 3x 3x 23
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 2x 3x 3x 3x 23 = 4968
Therefore, the value for common factors is 4968.
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 = 193314120480/(3x4968)
LCM = 193314120480/14904
LCM = 12970620
Thus, we can understand that the LCM of 780,723,828,414 is 12970620.
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FAQs on LCM of 780, 723, 828, 414
1. What is the LCM of 780, 723, 828, 414?
Answer: LCM of 780, 723, 828, 414 is 12970620.
2. How to calculate the LCM of 780, 723, 828, 414?
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 780, 723, 828, 414.
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}.