LCM of 510, 114, 342, 214, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 510, 114, 342, 214, 678 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, 114, 342, 214, 678. So, keep reading to learn more.
Given numbers are 510,114,342,214,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 510,114,342,214,678 is 351485370.
Find LCM of 510,114,342,214,678 with Prime Factorization
| 2 | 510, 114, 342, 214, 678 |
| 3 | 255, 57, 171, 107, 339 |
| 19 | 85, 19, 57, 107, 113 |
| 85, 1, 3, 107, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 19 x 85 x 1 x 3 x 107 x 113 = 351485370
Therefore, the lowest common multiple of 510,114,342,214,678 is 351485370.
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 114 x 342 x 214 x 678 = 2884991916960
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
114 : 1, 2, 3, 6, 19, 38, 57, 114
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
214 : 1, 2, 107, 214
678 : 1, 2, 3, 6, 113, 226, 339, 678
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 510,114,342,214,678, is 2.
Now, the common factors can be found like this.
510:2x 3x 5x 17
114:2x 3x 19
342:2x 3x 3x 19
214:2x 107
678:2x 3x 113
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 3x 3x 3x 19 = 4104
Therefore, the value for common factors is 4104.
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 = 2884991916960/(2x4104)
LCM = 2884991916960/8208
LCM = 351485370
Thus, we can understand that the LCM of 510,114,342,214,678 is 351485370.
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FAQs on LCM of 510, 114, 342, 214, 678
1. What is the LCM of 510, 114, 342, 214, 678?
Answer: LCM of 510, 114, 342, 214, 678 is 351485370.
2. How to calculate the LCM of 510, 114, 342, 214, 678?
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, 114, 342, 214, 678.
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}.