LCM of 360, 784, 217, 209
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 360, 784, 217, 209 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 360, 784, 217, 209. So, keep reading to learn more.
Given numbers are 360,784,217,209
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 360,784,217,209 is 228579120.
Find LCM of 360,784,217,209 with Prime Factorization
| 2 | 360, 784, 217, 209 |
| 2 | 180, 392, 217, 209 |
| 2 | 90, 196, 217, 209 |
| 7 | 45, 98, 217, 209 |
| 45, 14, 31, 209 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 7 x 45 x 14 x 31 x 209 = 228579120
Therefore, the lowest common multiple of 360,784,217,209 is 228579120.
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.
360 x 784 x 217 x 209 = 12800430720
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.
360 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
217 : 1, 7, 31, 217
209 : 1, 11, 19, 209
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 360,784,217,209, is 1.
Now, the common factors can be found like this.
360:2x 2x 2x 3x 3x 5
784:2x 2x 2x 2x 7x 7
217:7x 31
209:11x 19
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 7 = 56
Therefore, the value for common factors is 56.
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 = 12800430720/(1x56)
LCM = 12800430720/56
LCM = 228579120
Thus, we can understand that the LCM of 360,784,217,209 is 228579120.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 360, 784, 217, 209
1. What is the LCM of 360, 784, 217, 209?
Answer: LCM of 360, 784, 217, 209 is 228579120.
2. How to calculate the LCM of 360, 784, 217, 209?
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 360, 784, 217, 209.
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}.