LCM of 412, 585, 410, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 412, 585, 410, 312 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 412, 585, 410, 312. So, keep reading to learn more.
Given numbers are 412,585,410,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 412,585,410,312 is 19763640.
Find LCM of 412,585,410,312 with Prime Factorization
| 2 | 412, 585, 410, 312 |
| 2 | 206, 585, 205, 156 |
| 3 | 103, 585, 205, 78 |
| 5 | 103, 195, 205, 26 |
| 13 | 103, 39, 41, 26 |
| 103, 3, 41, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 13 x 103 x 3 x 41 x 2 = 19763640
Therefore, the lowest common multiple of 412,585,410,312 is 19763640.
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.
412 x 585 x 410 x 312 = 30831278400
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.
412 : 1, 2, 4, 103, 206, 412
585 : 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
410 : 1, 2, 5, 10, 41, 82, 205, 410
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 412,585,410,312, is 1.
Now, the common factors can be found like this.
412:2x 2x 103
585:3x 3x 5x 13
410:2x 5x 41
312:2x 2x 2x 3x 13
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 3x 5x 13 = 1560
Therefore, the value for common factors is 1560.
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 = 30831278400/(1x1560)
LCM = 30831278400/1560
LCM = 19763640
Thus, we can understand that the LCM of 412,585,410,312 is 19763640.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 412, 585, 410, 312
1. What is the LCM of 412, 585, 410, 312?
Answer: LCM of 412, 585, 410, 312 is 19763640.
2. How to calculate the LCM of 412, 585, 410, 312?
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 412, 585, 410, 312.
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}.