LCM of 408, 600, 519
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 408, 600, 519 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 408, 600, 519. So, keep reading to learn more.
Given numbers are 408,600,519
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 408,600,519 is 1764600.
Find LCM of 408,600,519 with Prime Factorization
| 2 | 408, 600, 519 |
| 2 | 204, 300, 519 |
| 2 | 102, 150, 519 |
| 3 | 51, 75, 519 |
| 17, 25, 173 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 17 x 25 x 173 = 1764600
Therefore, the lowest common multiple of 408,600,519 is 1764600.
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.
408 x 600 x 519 = 127051200
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.
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
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
519 : 1, 3, 173, 519
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 408,600,519, is 3.
Now, the common factors can be found like this.
408:2x 2x 2x 3x 17
600:2x 2x 2x 3x 5x 5
519:3x 173
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 3 = 24
Therefore, the value for common factors is 24.
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 = 127051200/(3x24)
LCM = 127051200/72
LCM = 1764600
Thus, we can understand that the LCM of 408,600,519 is 1764600.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 408, 600, 519
1. What is the LCM of 408, 600, 519?
Answer: LCM of 408, 600, 519 is 1764600.
2. How to calculate the LCM of 408, 600, 519?
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 408, 600, 519.
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}.