LCM of 519, 600, 414, 816
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 519, 600, 414, 816 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 519, 600, 414, 816. So, keep reading to learn more.
Given numbers are 519,600,414,816
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 519,600,414,816 is 243514800.
Find LCM of 519,600,414,816 with Prime Factorization
| 2 | 519, 600, 414, 816 |
| 2 | 519, 300, 207, 408 |
| 2 | 519, 150, 207, 204 |
| 3 | 519, 75, 207, 102 |
| 173, 25, 69, 34 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 173 x 25 x 69 x 34 = 243514800
Therefore, the lowest common multiple of 519,600,414,816 is 243514800.
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.
519 x 600 x 414 x 816 = 105198393600
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.
519 : 1, 3, 173, 519
600 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
816 : 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 519,600,414,816, is 3.
Now, the common factors can be found like this.
519:3x 173
600:2x 2x 2x 3x 5x 5
414:2x 3x 3x 23
816:2x 2x 2x 2x 3x 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 3x 3 = 144
Therefore, the value for common factors is 144.
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 = 105198393600/(3x144)
LCM = 105198393600/432
LCM = 243514800
Thus, we can understand that the LCM of 519,600,414,816 is 243514800.
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FAQs on LCM of 519, 600, 414, 816
1. What is the LCM of 519, 600, 414, 816?
Answer: LCM of 519, 600, 414, 816 is 243514800.
2. How to calculate the LCM of 519, 600, 414, 816?
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 519, 600, 414, 816.
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}.