LCM of 765, 108, 782, 306, 814
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 765, 108, 782, 306, 814 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 765, 108, 782, 306, 814. So, keep reading to learn more.
Given numbers are 765,108,782,306,814
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 765,108,782,306,814 is 85933980.
Find LCM of 765,108,782,306,814 with Prime Factorization
| 2 | 765, 108, 782, 306, 814 |
| 3 | 765, 54, 391, 153, 407 |
| 3 | 255, 18, 391, 51, 407 |
| 17 | 85, 6, 391, 17, 407 |
| 5, 6, 23, 1, 407 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 17 x 5 x 6 x 23 x 1 x 407 = 85933980
Therefore, the lowest common multiple of 765,108,782,306,814 is 85933980.
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.
765 x 108 x 782 x 306 x 814 = 16093028302560
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.
765 : 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
108 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
782 : 1, 2, 17, 23, 34, 46, 391, 782
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
814 : 1, 2, 11, 22, 37, 74, 407, 814
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 765,108,782,306,814, is 1.
Now, the common factors can be found like this.
765:3x 3x 5x 17
108:2x 2x 3x 3x 3
782:2x 17x 23
306:2x 3x 3x 17
814:2x 11x 37
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 3x 17x 17 = 187272
Therefore, the value for common factors is 187272.
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 = 16093028302560/(1x187272)
LCM = 16093028302560/187272
LCM = 85933980
Thus, we can understand that the LCM of 765,108,782,306,814 is 85933980.
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FAQs on LCM of 765, 108, 782, 306, 814
1. What is the LCM of 765, 108, 782, 306, 814?
Answer: LCM of 765, 108, 782, 306, 814 is 85933980.
2. How to calculate the LCM of 765, 108, 782, 306, 814?
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 765, 108, 782, 306, 814.
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}.