LCM of 468, 416, 540, 585
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 468, 416, 540, 585 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 468, 416, 540, 585. So, keep reading to learn more.
Given numbers are 468,416,540,585
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 468,416,540,585 is 56160.
Find LCM of 468,416,540,585 with Prime Factorization
| 2 | 468, 416, 540, 585 |
| 2 | 234, 208, 270, 585 |
| 3 | 117, 104, 135, 585 |
| 3 | 39, 104, 45, 195 |
| 5 | 13, 104, 15, 65 |
| 13 | 13, 104, 3, 13 |
| 1, 8, 3, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 13 x 1 x 8 x 3 x 1 = 56160
Therefore, the lowest common multiple of 468,416,540,585 is 56160.
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.
468 x 416 x 540 x 585 = 61501939200
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.
468 : 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
416 : 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
585 : 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 468,416,540,585, is 1.
Now, the common factors can be found like this.
468:2x 2x 3x 3x 13
416:2x 2x 2x 2x 2x 13
540:2x 2x 3x 3x 3x 5
585:3x 3x 5x 13
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 3x 3x 3x 3x 5x 13x 13 = 1095120
Therefore, the value for common factors is 1095120.
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 = 61501939200/(1x1095120)
LCM = 61501939200/1095120
LCM = 56160
Thus, we can understand that the LCM of 468,416,540,585 is 56160.
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FAQs on LCM of 468, 416, 540, 585
1. What is the LCM of 468, 416, 540, 585?
Answer: LCM of 468, 416, 540, 585 is 56160.
2. How to calculate the LCM of 468, 416, 540, 585?
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 468, 416, 540, 585.
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}.