LCM of 584, 412, 420, 610
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 584, 412, 420, 610 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 584, 412, 420, 610. So, keep reading to learn more.
Given numbers are 584,412,420,610
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 584,412,420,610 is 385273560.
Find LCM of 584,412,420,610 with Prime Factorization
| 2 | 584, 412, 420, 610 |
| 2 | 292, 206, 210, 305 |
| 5 | 146, 103, 105, 305 |
| 146, 103, 21, 61 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 5 x 146 x 103 x 21 x 61 = 385273560
Therefore, the lowest common multiple of 584,412,420,610 is 385273560.
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.
584 x 412 x 420 x 610 = 61643769600
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.
584 : 1, 2, 4, 8, 73, 146, 292, 584
412 : 1, 2, 4, 103, 206, 412
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
610 : 1, 2, 5, 10, 61, 122, 305, 610
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 584,412,420,610, is 2.
Now, the common factors can be found like this.
584:2x 2x 2x 73
412:2x 2x 103
420:2x 2x 3x 5x 7
610:2x 5x 61
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 5 = 80
Therefore, the value for common factors is 80.
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 = 61643769600/(2x80)
LCM = 61643769600/160
LCM = 385273560
Thus, we can understand that the LCM of 584,412,420,610 is 385273560.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 584, 412, 420, 610
1. What is the LCM of 584, 412, 420, 610?
Answer: LCM of 584, 412, 420, 610 is 385273560.
2. How to calculate the LCM of 584, 412, 420, 610?
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 584, 412, 420, 610.
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}.