LCM of 690, 678, 780, 512, 409
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 690, 678, 780, 512, 409 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 690, 678, 780, 512, 409. So, keep reading to learn more.
Given numbers are 690,678,780,512,409
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 690,678,780,512,409 is 106129021440.
Find LCM of 690,678,780,512,409 with Prime Factorization
| 2 | 690, 678, 780, 512, 409 |
| 2 | 345, 339, 390, 256, 409 |
| 3 | 345, 339, 195, 128, 409 |
| 5 | 115, 113, 65, 128, 409 |
| 23, 113, 13, 128, 409 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 23 x 113 x 13 x 128 x 409 = 106129021440
Therefore, the lowest common multiple of 690,678,780,512,409 is 106129021440.
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.
690 x 678 x 780 x 512 x 409 = 76412895436800
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.
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
678 : 1, 2, 3, 6, 113, 226, 339, 678
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
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
409 : 1, 409
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 690,678,780,512,409, is 1.
Now, the common factors can be found like this.
690:2x 3x 5x 23
678:2x 3x 113
780:2x 2x 3x 5x 13
512:2x 2x 2x 2x 2x 2x 2x 2x 2
409:409
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 2x 3x 3x 5 = 720
Therefore, the value for common factors is 720.
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 = 76412895436800/(1x720)
LCM = 76412895436800/720
LCM = 106129021440
Thus, we can understand that the LCM of 690,678,780,512,409 is 106129021440.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 690, 678, 780, 512, 409
1. What is the LCM of 690, 678, 780, 512, 409?
Answer: LCM of 690, 678, 780, 512, 409 is 106129021440.
2. How to calculate the LCM of 690, 678, 780, 512, 409?
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 690, 678, 780, 512, 409.
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}.