LCM of 720, 864, 209, 512
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 720, 864, 209, 512 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 720, 864, 209, 512. So, keep reading to learn more.
Given numbers are 720,864,209,512
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 720,864,209,512 is 14446080.
Find LCM of 720,864,209,512 with Prime Factorization
| 2 | 720, 864, 209, 512 |
| 2 | 360, 432, 209, 256 |
| 2 | 180, 216, 209, 128 |
| 2 | 90, 108, 209, 64 |
| 2 | 45, 54, 209, 32 |
| 3 | 45, 27, 209, 16 |
| 3 | 15, 9, 209, 16 |
| 5, 3, 209, 16 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 3 x 209 x 16 = 14446080
Therefore, the lowest common multiple of 720,864,209,512 is 14446080.
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.
720 x 864 x 209 x 512 = 66567536640
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.
720 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
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
209 : 1, 11, 19, 209
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 720,864,209,512, is 1.
Now, the common factors can be found like this.
720:2x 2x 2x 2x 3x 3x 5
864:2x 2x 2x 2x 2x 3x 3x 3
209:11x 19
512:2x 2x 2x 2x 2x 2x 2x 2x 2
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 2x 2x 2x 3x 3 = 4608
Therefore, the value for common factors is 4608.
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 = 66567536640/(1x4608)
LCM = 66567536640/4608
LCM = 14446080
Thus, we can understand that the LCM of 720,864,209,512 is 14446080.
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FAQs on LCM of 720, 864, 209, 512
1. What is the LCM of 720, 864, 209, 512?
Answer: LCM of 720, 864, 209, 512 is 14446080.
2. How to calculate the LCM of 720, 864, 209, 512?
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 720, 864, 209, 512.
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}.