LCM of 864, 185, 642, 690, 920
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 864, 185, 642, 690, 920 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 864, 185, 642, 690, 920. So, keep reading to learn more.
Given numbers are 864,185,642,690,920
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 864,185,642,690,920 is 393366240.
Find LCM of 864,185,642,690,920 with Prime Factorization
| 2 | 864, 185, 642, 690, 920 |
| 2 | 432, 185, 321, 345, 460 |
| 2 | 216, 185, 321, 345, 230 |
| 3 | 108, 185, 321, 345, 115 |
| 5 | 36, 185, 107, 115, 115 |
| 23 | 36, 37, 107, 23, 23 |
| 36, 37, 107, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 23 x 36 x 37 x 107 x 1 x 1 = 393366240
Therefore, the lowest common multiple of 864,185,642,690,920 is 393366240.
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.
864 x 185 x 642 x 690 x 920 = 65141449344000
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.
864 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
185 : 1, 5, 37, 185
642 : 1, 2, 3, 6, 107, 214, 321, 642
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
920 : 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 864,185,642,690,920, is 1.
Now, the common factors can be found like this.
864:2x 2x 2x 2x 2x 3x 3x 3
185:5x 37
642:2x 3x 107
690:2x 3x 5x 23
920:2x 2x 2x 5x 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 2x 2x 3x 3x 5x 5x 23 = 165600
Therefore, the value for common factors is 165600.
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 = 65141449344000/(1x165600)
LCM = 65141449344000/165600
LCM = 393366240
Thus, we can understand that the LCM of 864,185,642,690,920 is 393366240.
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FAQs on LCM of 864, 185, 642, 690, 920
1. What is the LCM of 864, 185, 642, 690, 920?
Answer: LCM of 864, 185, 642, 690, 920 is 393366240.
2. How to calculate the LCM of 864, 185, 642, 690, 920?
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 864, 185, 642, 690, 920.
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}.