LCM of 305, 810, 403, 138
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 305, 810, 403, 138 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, 810, 403, 138. So, keep reading to learn more.
Given numbers are 305,810,403,138
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 305,810,403,138 is 457981290.
Find LCM of 305,810,403,138 with Prime Factorization
| 2 | 305, 810, 403, 138 |
| 3 | 305, 405, 403, 69 |
| 5 | 305, 135, 403, 23 |
| 61, 27, 403, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 61 x 27 x 403 x 23 = 457981290
Therefore, the lowest common multiple of 305,810,403,138 is 457981290.
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 810 x 403 x 138 = 13739438700
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
810 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
403 : 1, 13, 31, 403
138 : 1, 2, 3, 6, 23, 46, 69, 138
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 305,810,403,138, is 1.
Now, the common factors can be found like this.
305:5x 61
810:2x 3x 3x 3x 3x 5
403:13x 31
138:2x 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 3x 5 = 30
Therefore, the value for common factors is 30.
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 = 13739438700/(1x30)
LCM = 13739438700/30
LCM = 457981290
Thus, we can understand that the LCM of 305,810,403,138 is 457981290.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 305, 810, 403, 138
1. What is the LCM of 305, 810, 403, 138?
Answer: LCM of 305, 810, 403, 138 is 457981290.
2. How to calculate the LCM of 305, 810, 403, 138?
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, 810, 403, 138.
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}.