LCM of 205, 835, 420, 690, 825
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 205, 835, 420, 690, 825 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 205, 835, 420, 690, 825. So, keep reading to learn more.
Given numbers are 205,835,420,690,825
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 205,835,420,690,825 is 3637811100.
Find LCM of 205,835,420,690,825 with Prime Factorization
| 2 | 205, 835, 420, 690, 825 |
| 3 | 205, 835, 210, 345, 825 |
| 5 | 205, 835, 70, 115, 275 |
| 41, 167, 14, 23, 55 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 41 x 167 x 14 x 23 x 55 = 3637811100
Therefore, the lowest common multiple of 205,835,420,690,825 is 3637811100.
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.
205 x 835 x 420 x 690 x 825 = 40925374875000
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.
205 : 1, 5, 41, 205
835 : 1, 5, 167, 835
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
825 : 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
5 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 205,835,420,690,825, is 5.
Now, the common factors can be found like this.
205:5x 41
835:5x 167
420:2x 2x 3x 5x 7
690:2x 3x 5x 23
825:3x 5x 5x 11
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 3x 5x 5x 5 = 2250
Therefore, the value for common factors is 2250.
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 = 40925374875000/(5x2250)
LCM = 40925374875000/11250
LCM = 3637811100
Thus, we can understand that the LCM of 205,835,420,690,825 is 3637811100.
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FAQs on LCM of 205, 835, 420, 690, 825
1. What is the LCM of 205, 835, 420, 690, 825?
Answer: LCM of 205, 835, 420, 690, 825 is 3637811100.
2. How to calculate the LCM of 205, 835, 420, 690, 825?
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 205, 835, 420, 690, 825.
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}.