LCM of 578, 405, 748, 461, 648
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 578, 405, 748, 461, 648 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 578, 405, 748, 461, 648. So, keep reading to learn more.
Given numbers are 578,405,748,461,648
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 578,405,748,461,648 is 4748281560.
Find LCM of 578,405,748,461,648 with Prime Factorization
| 2 | 578, 405, 748, 461, 648 |
| 2 | 289, 405, 374, 461, 324 |
| 3 | 289, 405, 187, 461, 162 |
| 3 | 289, 135, 187, 461, 54 |
| 3 | 289, 45, 187, 461, 18 |
| 3 | 289, 15, 187, 461, 6 |
| 17 | 289, 5, 187, 461, 2 |
| 17, 5, 11, 461, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 3 x 17 x 17 x 5 x 11 x 461 x 2 = 4748281560
Therefore, the lowest common multiple of 578,405,748,461,648 is 4748281560.
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.
578 x 405 x 748 x 461 x 648 = 52307069664960
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.
578 : 1, 2, 17, 34, 289, 578
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
748 : 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
461 : 1, 461
648 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 578,405,748,461,648, is 1.
Now, the common factors can be found like this.
578:2x 17x 17
405:3x 3x 3x 3x 5
748:2x 2x 11x 17
461:461
648:2x 2x 2x 3x 3x 3x 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 2x 3x 3x 3x 3x 17 = 11016
Therefore, the value for common factors is 11016.
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 = 52307069664960/(1x11016)
LCM = 52307069664960/11016
LCM = 4748281560
Thus, we can understand that the LCM of 578,405,748,461,648 is 4748281560.
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FAQs on LCM of 578, 405, 748, 461, 648
1. What is the LCM of 578, 405, 748, 461, 648?
Answer: LCM of 578, 405, 748, 461, 648 is 4748281560.
2. How to calculate the LCM of 578, 405, 748, 461, 648?
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 578, 405, 748, 461, 648.
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}.