LCM of 304, 209, 684, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 304, 209, 684, 414 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 304, 209, 684, 414. So, keep reading to learn more.
Given numbers are 304,209,684,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 304,209,684,414 is 692208.
Find LCM of 304,209,684,414 with Prime Factorization
| 2 | 304, 209, 684, 414 |
| 2 | 152, 209, 342, 207 |
| 3 | 76, 209, 171, 207 |
| 3 | 76, 209, 57, 69 |
| 19 | 76, 209, 19, 23 |
| 4, 11, 1, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 19 x 4 x 11 x 1 x 23 = 692208
Therefore, the lowest common multiple of 304,209,684,414 is 692208.
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.
304 x 209 x 684 x 414 = 17991870336
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.
304 : 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
209 : 1, 11, 19, 209
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 304,209,684,414, is 1.
Now, the common factors can be found like this.
304:2x 2x 2x 2x 19
209:11x 19
684:2x 2x 3x 3x 19
414:2x 3x 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 2x 2x 3x 3x 19x 19 = 25992
Therefore, the value for common factors is 25992.
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 = 17991870336/(1x25992)
LCM = 17991870336/25992
LCM = 692208
Thus, we can understand that the LCM of 304,209,684,414 is 692208.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 304, 209, 684, 414
1. What is the LCM of 304, 209, 684, 414?
Answer: LCM of 304, 209, 684, 414 is 692208.
2. How to calculate the LCM of 304, 209, 684, 414?
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 304, 209, 684, 414.
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}.