LCM of 205, 408, 978, 374, 321
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 205, 408, 978, 374, 321 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, 408, 978, 374, 321. So, keep reading to learn more.
Given numbers are 205,408,978,374,321
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 205,408,978,374,321 is 16046417640.
Find LCM of 205,408,978,374,321 with Prime Factorization
| 2 | 205, 408, 978, 374, 321 |
| 3 | 205, 204, 489, 187, 321 |
| 17 | 205, 68, 163, 187, 107 |
| 205, 4, 163, 11, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 17 x 205 x 4 x 163 x 11 x 107 = 16046417640
Therefore, the lowest common multiple of 205,408,978,374,321 is 16046417640.
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 408 x 978 x 374 x 321 = 9820407595680
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
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
978 : 1, 2, 3, 6, 163, 326, 489, 978
374 : 1, 2, 11, 17, 22, 34, 187, 374
321 : 1, 3, 107, 321
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 205,408,978,374,321, is 1.
Now, the common factors can be found like this.
205:5x 41
408:2x 2x 2x 3x 17
978:2x 3x 163
374:2x 11x 17
321:3x 107
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 3x 3x 17 = 612
Therefore, the value for common factors is 612.
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 = 9820407595680/(1x612)
LCM = 9820407595680/612
LCM = 16046417640
Thus, we can understand that the LCM of 205,408,978,374,321 is 16046417640.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 205, 408, 978, 374, 321
1. What is the LCM of 205, 408, 978, 374, 321?
Answer: LCM of 205, 408, 978, 374, 321 is 16046417640.
2. How to calculate the LCM of 205, 408, 978, 374, 321?
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, 408, 978, 374, 321.
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}.