LCM of 414, 204, 689, 294, 731
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 414, 204, 689, 294, 731 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 414, 204, 689, 294, 731. So, keep reading to learn more.
Given numbers are 414,204,689,294,731
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 414,204,689,294,731 is 20434452948.
Find LCM of 414,204,689,294,731 with Prime Factorization
| 2 | 414, 204, 689, 294, 731 |
| 3 | 207, 102, 689, 147, 731 |
| 17 | 69, 34, 689, 49, 731 |
| 69, 2, 689, 49, 43 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 17 x 69 x 2 x 689 x 49 x 43 = 20434452948
Therefore, the lowest common multiple of 414,204,689,294,731 is 20434452948.
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.
414 x 204 x 689 x 294 x 731 = 12505885204176
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.
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
204 : 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
689 : 1, 13, 53, 689
294 : 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
731 : 1, 17, 43, 731
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 414,204,689,294,731, is 1.
Now, the common factors can be found like this.
414:2x 3x 3x 23
204:2x 2x 3x 17
689:13x 53
294:2x 3x 7x 7
731:17x 43
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 = 12505885204176/(1x612)
LCM = 12505885204176/612
LCM = 20434452948
Thus, we can understand that the LCM of 414,204,689,294,731 is 20434452948.
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FAQs on LCM of 414, 204, 689, 294, 731
1. What is the LCM of 414, 204, 689, 294, 731?
Answer: LCM of 414, 204, 689, 294, 731 is 20434452948.
2. How to calculate the LCM of 414, 204, 689, 294, 731?
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 414, 204, 689, 294, 731.
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}.