LCM of 728, 105, 390, 392
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 728, 105, 390, 392 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 728, 105, 390, 392. So, keep reading to learn more.
Given numbers are 728,105,390,392
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 728,105,390,392 is 76440.
Find LCM of 728,105,390,392 with Prime Factorization
| 2 | 728, 105, 390, 392 |
| 2 | 364, 105, 195, 196 |
| 2 | 182, 105, 195, 98 |
| 3 | 91, 105, 195, 49 |
| 5 | 91, 35, 65, 49 |
| 7 | 91, 7, 13, 49 |
| 13 | 13, 1, 13, 7 |
| 1, 1, 1, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 13 x 1 x 1 x 1 x 7 = 76440
Therefore, the lowest common multiple of 728,105,390,392 is 76440.
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.
728 x 105 x 390 x 392 = 11686147200
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.
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
105 : 1, 3, 5, 7, 15, 21, 35, 105
390 : 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
392 : 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 728,105,390,392, is 1.
Now, the common factors can be found like this.
728:2x 2x 2x 7x 13
105:3x 5x 7
390:2x 3x 5x 13
392:2x 2x 2x 7x 7
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 3x 5x 7x 7x 13 = 152880
Therefore, the value for common factors is 152880.
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 = 11686147200/(1x152880)
LCM = 11686147200/152880
LCM = 76440
Thus, we can understand that the LCM of 728,105,390,392 is 76440.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 728, 105, 390, 392
1. What is the LCM of 728, 105, 390, 392?
Answer: LCM of 728, 105, 390, 392 is 76440.
2. How to calculate the LCM of 728, 105, 390, 392?
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 728, 105, 390, 392.
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}.