LCM of 460, 522, 768, 405
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 460, 522, 768, 405 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, 522, 768, 405. So, keep reading to learn more.
Given numbers are 460,522,768,405
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 460,522,768,405 is 69154560.
Find LCM of 460,522,768,405 with Prime Factorization
| 2 | 460, 522, 768, 405 |
| 2 | 230, 261, 384, 405 |
| 3 | 115, 261, 192, 405 |
| 3 | 115, 87, 64, 135 |
| 5 | 115, 29, 64, 45 |
| 23, 29, 64, 9 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 23 x 29 x 64 x 9 = 69154560
Therefore, the lowest common multiple of 460,522,768,405 is 69154560.
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 522 x 768 x 405 = 74686924800
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
522 : 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 460,522,768,405, is 1.
Now, the common factors can be found like this.
460:2x 2x 5x 23
522:2x 3x 3x 29
768:2x 2x 2x 2x 2x 2x 2x 2x 3
405:3x 3x 3x 3x 5
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 5 = 1080
Therefore, the value for common factors is 1080.
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 = 74686924800/(1x1080)
LCM = 74686924800/1080
LCM = 69154560
Thus, we can understand that the LCM of 460,522,768,405 is 69154560.
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FAQs on LCM of 460, 522, 768, 405
1. What is the LCM of 460, 522, 768, 405?
Answer: LCM of 460, 522, 768, 405 is 69154560.
2. How to calculate the LCM of 460, 522, 768, 405?
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, 522, 768, 405.
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}.