LCM of 460, 419, 731, 705, 768
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 460, 419, 731, 705, 768 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 460, 419, 731, 705, 768. So, keep reading to learn more.
Given numbers are 460,419,731,705,768
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 460,419,731,705,768 is 1271417890560.
Find LCM of 460,419,731,705,768 with Prime Factorization
| 2 | 460, 419, 731, 705, 768 |
| 2 | 230, 419, 731, 705, 384 |
| 3 | 115, 419, 731, 705, 192 |
| 5 | 115, 419, 731, 235, 64 |
| 23, 419, 731, 47, 64 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 23 x 419 x 731 x 47 x 64 = 1271417890560
Therefore, the lowest common multiple of 460,419,731,705,768 is 1271417890560.
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.
460 x 419 x 731 x 705 x 768 = 76285073433600
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.
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
419 : 1, 419
731 : 1, 17, 43, 731
705 : 1, 3, 5, 15, 47, 141, 235, 705
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 460,419,731,705,768, is 1.
Now, the common factors can be found like this.
460:2x 2x 5x 23
419:419
731:17x 43
705:3x 5x 47
768:2x 2x 2x 2x 2x 2x 2x 2x 3
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 3x 5 = 60
Therefore, the value for common factors is 60.
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 = 76285073433600/(1x60)
LCM = 76285073433600/60
LCM = 1271417890560
Thus, we can understand that the LCM of 460,419,731,705,768 is 1271417890560.
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FAQs on LCM of 460, 419, 731, 705, 768
1. What is the LCM of 460, 419, 731, 705, 768?
Answer: LCM of 460, 419, 731, 705, 768 is 1271417890560.
2. How to calculate the LCM of 460, 419, 731, 705, 768?
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 460, 419, 731, 705, 768.
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}.