LCM of 405, 715, 312, 645
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 405, 715, 312, 645 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 405, 715, 312, 645. So, keep reading to learn more.
Given numbers are 405,715,312,645
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 405,715,312,645 is 19922760.
Find LCM of 405,715,312,645 with Prime Factorization
| 3 | 405, 715, 312, 645 |
| 5 | 135, 715, 104, 215 |
| 13 | 27, 143, 104, 43 |
| 27, 11, 8, 43 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 13 x 27 x 11 x 8 x 43 = 19922760
Therefore, the lowest common multiple of 405,715,312,645 is 19922760.
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.
405 x 715 x 312 x 645 = 58274073000
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.
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
715 : 1, 5, 11, 13, 55, 65, 143, 715
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
645 : 1, 3, 5, 15, 43, 129, 215, 645
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 405,715,312,645, is 1.
Now, the common factors can be found like this.
405:3x 3x 3x 3x 5
715:5x 11x 13
312:2x 2x 2x 3x 13
645:3x 5x 43
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 3x 5x 5x 13 = 2925
Therefore, the value for common factors is 2925.
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 = 58274073000/(1x2925)
LCM = 58274073000/2925
LCM = 19922760
Thus, we can understand that the LCM of 405,715,312,645 is 19922760.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 405, 715, 312, 645
1. What is the LCM of 405, 715, 312, 645?
Answer: LCM of 405, 715, 312, 645 is 19922760.
2. How to calculate the LCM of 405, 715, 312, 645?
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 405, 715, 312, 645.
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}.