LCM of 510, 408, 858, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 510, 408, 858, 312 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 510, 408, 858, 312. So, keep reading to learn more.
Given numbers are 510,408,858,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 510,408,858,312 is 291720.
Find LCM of 510,408,858,312 with Prime Factorization
| 2 | 510, 408, 858, 312 |
| 2 | 255, 204, 429, 156 |
| 2 | 255, 102, 429, 78 |
| 3 | 255, 51, 429, 39 |
| 13 | 85, 17, 143, 13 |
| 17 | 85, 17, 11, 1 |
| 5, 1, 11, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 13 x 17 x 5 x 1 x 11 x 1 = 291720
Therefore, the lowest common multiple of 510,408,858,312 is 291720.
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.
510 x 408 x 858 x 312 = 55702183680
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.
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
858 : 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 510,408,858,312, is 6.
Now, the common factors can be found like this.
510:2x 3x 5x 17
408:2x 2x 2x 3x 17
858:2x 3x 11x 13
312:2x 2x 2x 3x 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 13x 17 = 31824
Therefore, the value for common factors is 31824.
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 = 55702183680/(6x31824)
LCM = 55702183680/190944
LCM = 291720
Thus, we can understand that the LCM of 510,408,858,312 is 291720.
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FAQs on LCM of 510, 408, 858, 312
1. What is the LCM of 510, 408, 858, 312?
Answer: LCM of 510, 408, 858, 312 is 291720.
2. How to calculate the LCM of 510, 408, 858, 312?
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 510, 408, 858, 312.
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}.