LCM of 516, 234, 478, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 516, 234, 478, 414 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 516, 234, 478, 414. So, keep reading to learn more.
Given numbers are 516,234,478,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 516,234,478,414 is 110621628.
Find LCM of 516,234,478,414 with Prime Factorization
| 2 | 516, 234, 478, 414 |
| 3 | 258, 117, 239, 207 |
| 3 | 86, 39, 239, 69 |
| 86, 13, 239, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 86 x 13 x 239 x 23 = 110621628
Therefore, the lowest common multiple of 516,234,478,414 is 110621628.
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.
516 x 234 x 478 x 414 = 23894271648
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.
516 : 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
234 : 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
478 : 1, 2, 239, 478
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 516,234,478,414, is 2.
Now, the common factors can be found like this.
516:2x 2x 3x 43
234:2x 3x 3x 13
478:2x 239
414:2x 3x 3x 23
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 3x 3x 3 = 108
Therefore, the value for common factors is 108.
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 = 23894271648/(2x108)
LCM = 23894271648/216
LCM = 110621628
Thus, we can understand that the LCM of 516,234,478,414 is 110621628.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 516, 234, 478, 414
1. What is the LCM of 516, 234, 478, 414?
Answer: LCM of 516, 234, 478, 414 is 110621628.
2. How to calculate the LCM of 516, 234, 478, 414?
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 516, 234, 478, 414.
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}.