LCM of 784, 345, 204, 217
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 784, 345, 204, 217 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 784, 345, 204, 217. So, keep reading to learn more.
Given numbers are 784,345,204,217
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 784,345,204,217 is 142542960.
Find LCM of 784,345,204,217 with Prime Factorization
| 2 | 784, 345, 204, 217 |
| 2 | 392, 345, 102, 217 |
| 3 | 196, 345, 51, 217 |
| 7 | 196, 115, 17, 217 |
| 28, 115, 17, 31 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 28 x 115 x 17 x 31 = 142542960
Therefore, the lowest common multiple of 784,345,204,217 is 142542960.
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.
784 x 345 x 204 x 217 = 11973608640
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.
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
345 : 1, 3, 5, 15, 23, 69, 115, 345
204 : 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
217 : 1, 7, 31, 217
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 784,345,204,217, is 1.
Now, the common factors can be found like this.
784:2x 2x 2x 2x 7x 7
345:3x 5x 23
204:2x 2x 3x 17
217:7x 31
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 7 = 84
Therefore, the value for common factors is 84.
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 = 11973608640/(1x84)
LCM = 11973608640/84
LCM = 142542960
Thus, we can understand that the LCM of 784,345,204,217 is 142542960.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 784, 345, 204, 217
1. What is the LCM of 784, 345, 204, 217?
Answer: LCM of 784, 345, 204, 217 is 142542960.
2. How to calculate the LCM of 784, 345, 204, 217?
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 784, 345, 204, 217.
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}.