LCM of 416, 400, 576, 289
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 416, 400, 576, 289 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 416, 400, 576, 289. So, keep reading to learn more.
Given numbers are 416,400,576,289
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 416,400,576,289 is 54100800.
Find LCM of 416,400,576,289 with Prime Factorization
| 2 | 416, 400, 576, 289 |
| 2 | 208, 200, 288, 289 |
| 2 | 104, 100, 144, 289 |
| 2 | 52, 50, 72, 289 |
| 2 | 26, 25, 36, 289 |
| 13, 25, 18, 289 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 13 x 25 x 18 x 289 = 54100800
Therefore, the lowest common multiple of 416,400,576,289 is 54100800.
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.
416 x 400 x 576 x 289 = 27699609600
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.
416 : 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
289 : 1, 17, 289
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 416,400,576,289, is 1.
Now, the common factors can be found like this.
416:2x 2x 2x 2x 2x 13
400:2x 2x 2x 2x 5x 5
576:2x 2x 2x 2x 2x 2x 3x 3
289:17x 17
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 2x 2x 2x 2x 2 = 512
Therefore, the value for common factors is 512.
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 = 27699609600/(1x512)
LCM = 27699609600/512
LCM = 54100800
Thus, we can understand that the LCM of 416,400,576,289 is 54100800.
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FAQs on LCM of 416, 400, 576, 289
1. What is the LCM of 416, 400, 576, 289?
Answer: LCM of 416, 400, 576, 289 is 54100800.
2. How to calculate the LCM of 416, 400, 576, 289?
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 416, 400, 576, 289.
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}.