LCM of 408, 512, 313, 289
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 408, 512, 313, 289 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 408, 512, 313, 289. So, keep reading to learn more.
Given numbers are 408,512,313,289
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 408,512,313,289 is 138941952.
Find LCM of 408,512,313,289 with Prime Factorization
| 2 | 408, 512, 313, 289 |
| 2 | 204, 256, 313, 289 |
| 2 | 102, 128, 313, 289 |
| 17 | 51, 64, 313, 289 |
| 3, 64, 313, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 17 x 3 x 64 x 313 x 17 = 138941952
Therefore, the lowest common multiple of 408,512,313,289 is 138941952.
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.
408 x 512 x 313 x 289 = 18896105472
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.
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
313 : 1, 313
289 : 1, 17, 289
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 408,512,313,289, is 1.
Now, the common factors can be found like this.
408:2x 2x 2x 3x 17
512:2x 2x 2x 2x 2x 2x 2x 2x 2
313:313
289:17x 17
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 17 = 136
Therefore, the value for common factors is 136.
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 = 18896105472/(1x136)
LCM = 18896105472/136
LCM = 138941952
Thus, we can understand that the LCM of 408,512,313,289 is 138941952.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 408, 512, 313, 289
1. What is the LCM of 408, 512, 313, 289?
Answer: LCM of 408, 512, 313, 289 is 138941952.
2. How to calculate the LCM of 408, 512, 313, 289?
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 408, 512, 313, 289.
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}.