LCM of 305, 670, 900, 412
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 305, 670, 900, 412 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 305, 670, 900, 412. So, keep reading to learn more.
Given numbers are 305,670,900,412
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 305,670,900,412 is 378864900.
Find LCM of 305,670,900,412 with Prime Factorization
| 2 | 305, 670, 900, 412 |
| 2 | 305, 335, 450, 206 |
| 5 | 305, 335, 225, 103 |
| 61, 67, 45, 103 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 5 x 61 x 67 x 45 x 103 = 378864900
Therefore, the lowest common multiple of 305,670,900,412 is 378864900.
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.
305 x 670 x 900 x 412 = 75772980000
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.
305 : 1, 5, 61, 305
670 : 1, 2, 5, 10, 67, 134, 335, 670
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
412 : 1, 2, 4, 103, 206, 412
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 305,670,900,412, is 1.
Now, the common factors can be found like this.
305:5x 61
670:2x 5x 67
900:2x 2x 3x 3x 5x 5
412:2x 2x 103
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 5x 5 = 200
Therefore, the value for common factors is 200.
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 = 75772980000/(1x200)
LCM = 75772980000/200
LCM = 378864900
Thus, we can understand that the LCM of 305,670,900,412 is 378864900.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 305, 670, 900, 412
1. What is the LCM of 305, 670, 900, 412?
Answer: LCM of 305, 670, 900, 412 is 378864900.
2. How to calculate the LCM of 305, 670, 900, 412?
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 305, 670, 900, 412.
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}.