LCM of 306, 420, 870, 417
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 306, 420, 870, 417 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 306, 420, 870, 417. So, keep reading to learn more.
Given numbers are 306,420,870,417
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 306,420,870,417 is 86344020.
Find LCM of 306,420,870,417 with Prime Factorization
| 2 | 306, 420, 870, 417 |
| 3 | 153, 210, 435, 417 |
| 5 | 51, 70, 145, 139 |
| 51, 14, 29, 139 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 51 x 14 x 29 x 139 = 86344020
Therefore, the lowest common multiple of 306,420,870,417 is 86344020.
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.
306 x 420 x 870 x 417 = 46625770800
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.
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
870 : 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
417 : 1, 3, 139, 417
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 306,420,870,417, is 3.
Now, the common factors can be found like this.
306:2x 3x 3x 17
420:2x 2x 3x 5x 7
870:2x 3x 5x 29
417:3x 139
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 5 = 180
Therefore, the value for common factors is 180.
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 = 46625770800/(3x180)
LCM = 46625770800/540
LCM = 86344020
Thus, we can understand that the LCM of 306,420,870,417 is 86344020.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 306, 420, 870, 417
1. What is the LCM of 306, 420, 870, 417?
Answer: LCM of 306, 420, 870, 417 is 86344020.
2. How to calculate the LCM of 306, 420, 870, 417?
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 306, 420, 870, 417.
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}.