LCM of 414, 450, 105, 814
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 414, 450, 105, 814 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 414, 450, 105, 814. So, keep reading to learn more.
Given numbers are 414,450,105,814
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 414,450,105,814 is 29487150.
Find LCM of 414,450,105,814 with Prime Factorization
| 2 | 414, 450, 105, 814 |
| 3 | 207, 225, 105, 407 |
| 3 | 69, 75, 35, 407 |
| 5 | 23, 25, 35, 407 |
| 23, 5, 7, 407 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 5 x 23 x 5 x 7 x 407 = 29487150
Therefore, the lowest common multiple of 414,450,105,814 is 29487150.
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.
414 x 450 x 105 x 814 = 15923061000
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.
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
450 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
105 : 1, 3, 5, 7, 15, 21, 35, 105
814 : 1, 2, 11, 22, 37, 74, 407, 814
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 414,450,105,814, is 1.
Now, the common factors can be found like this.
414:2x 3x 3x 23
450:2x 3x 3x 5x 5
105:3x 5x 7
814:2x 11x 37
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 3x 5 = 540
Therefore, the value for common factors is 540.
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 = 15923061000/(1x540)
LCM = 15923061000/540
LCM = 29487150
Thus, we can understand that the LCM of 414,450,105,814 is 29487150.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 414, 450, 105, 814
1. What is the LCM of 414, 450, 105, 814?
Answer: LCM of 414, 450, 105, 814 is 29487150.
2. How to calculate the LCM of 414, 450, 105, 814?
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 414, 450, 105, 814.
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}.