LCM of 680, 414, 200, 374, 825
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 680, 414, 200, 374, 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 680, 414, 200, 374, 825. So, keep reading to learn more.
Given numbers are 680,414,200,374,825
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 680,414,200,374,825 is 7741800.
Find LCM of 680,414,200,374,825 with Prime Factorization
| 2 | 680, 414, 200, 374, 825 |
| 2 | 340, 207, 100, 187, 825 |
| 2 | 170, 207, 50, 187, 825 |
| 3 | 85, 207, 25, 187, 825 |
| 5 | 85, 69, 25, 187, 275 |
| 5 | 17, 69, 5, 187, 55 |
| 11 | 17, 69, 1, 187, 11 |
| 17 | 17, 69, 1, 17, 1 |
| 1, 69, 1, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 5 x 11 x 17 x 1 x 69 x 1 x 1 x 1 = 7741800
Therefore, the lowest common multiple of 680,414,200,374,825 is 7741800.
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.
680 x 414 x 200 x 374 x 825 = 17372599200000
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.
680 : 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
374 : 1, 2, 11, 17, 22, 34, 187, 374
825 : 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 680,414,200,374,825, is 1.
Now, the common factors can be found like this.
680:2x 2x 2x 5x 17
414:2x 3x 3x 23
200:2x 2x 2x 5x 5
374:2x 11x 17
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 2x 2x 2x 2x 3x 5x 5x 5x 11x 17 = 2244000
Therefore, the value for common factors is 2244000.
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 = 17372599200000/(1x2244000)
LCM = 17372599200000/2244000
LCM = 7741800
Thus, we can understand that the LCM of 680,414,200,374,825 is 7741800.
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FAQs on LCM of 680, 414, 200, 374, 825
1. What is the LCM of 680, 414, 200, 374, 825?
Answer: LCM of 680, 414, 200, 374, 825 is 7741800.
2. How to calculate the LCM of 680, 414, 200, 374, 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 680, 414, 200, 374, 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}.