LCM of 412, 418, 309, 106, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 412, 418, 309, 106, 105 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 412, 418, 309, 106, 105. So, keep reading to learn more.
Given numbers are 412,418,309,106,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 412,418,309,106,105 is 479191020.
Find LCM of 412,418,309,106,105 with Prime Factorization
| 2 | 412, 418, 309, 106, 105 |
| 3 | 206, 209, 309, 53, 105 |
| 103 | 206, 209, 103, 53, 35 |
| 2, 209, 1, 53, 35 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 103 x 2 x 209 x 1 x 53 x 35 = 479191020
Therefore, the lowest common multiple of 412,418,309,106,105 is 479191020.
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.
412 x 418 x 309 x 106 x 105 = 592280100720
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.
412 : 1, 2, 4, 103, 206, 412
418 : 1, 2, 11, 19, 22, 38, 209, 418
309 : 1, 3, 103, 309
106 : 1, 2, 53, 106
105 : 1, 3, 5, 7, 15, 21, 35, 105
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 412,418,309,106,105, is 1.
Now, the common factors can be found like this.
412:2x 2x 103
418:2x 11x 19
309:3x 103
106:2x 53
105:3x 5x 7
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 103 = 1236
Therefore, the value for common factors is 1236.
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 = 592280100720/(1x1236)
LCM = 592280100720/1236
LCM = 479191020
Thus, we can understand that the LCM of 412,418,309,106,105 is 479191020.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 412, 418, 309, 106, 105
1. What is the LCM of 412, 418, 309, 106, 105?
Answer: LCM of 412, 418, 309, 106, 105 is 479191020.
2. How to calculate the LCM of 412, 418, 309, 106, 105?
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 412, 418, 309, 106, 105.
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}.