LCM of 432, 204, 314, 864
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 432, 204, 314, 864 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 432, 204, 314, 864. So, keep reading to learn more.
Given numbers are 432,204,314,864
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 432,204,314,864 is 2306016.
Find LCM of 432,204,314,864 with Prime Factorization
| 2 | 432, 204, 314, 864 |
| 2 | 216, 102, 157, 432 |
| 2 | 108, 51, 157, 216 |
| 2 | 54, 51, 157, 108 |
| 3 | 27, 51, 157, 54 |
| 3 | 9, 17, 157, 18 |
| 3 | 3, 17, 157, 6 |
| 1, 17, 157, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 3 x 1 x 17 x 157 x 2 = 2306016
Therefore, the lowest common multiple of 432,204,314,864 is 2306016.
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.
432 x 204 x 314 x 864 = 23908773888
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.
432 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
204 : 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
314 : 1, 2, 157, 314
864 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 432,204,314,864, is 2.
Now, the common factors can be found like this.
432:2x 2x 2x 2x 3x 3x 3
204:2x 2x 3x 17
314:2x 157
864:2x 2x 2x 2x 2x 3x 3x 3
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 2x 2x 2x 3x 3x 3x 3 = 5184
Therefore, the value for common factors is 5184.
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 = 23908773888/(2x5184)
LCM = 23908773888/10368
LCM = 2306016
Thus, we can understand that the LCM of 432,204,314,864 is 2306016.
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FAQs on LCM of 432, 204, 314, 864
1. What is the LCM of 432, 204, 314, 864?
Answer: LCM of 432, 204, 314, 864 is 2306016.
2. How to calculate the LCM of 432, 204, 314, 864?
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 432, 204, 314, 864.
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}.