LCM of 416, 255, 282, 115, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 416, 255, 282, 115, 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 416, 255, 282, 115, 312. So, keep reading to learn more.
Given numbers are 416,255,282,115,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 416,255,282,115,312 is 114672480.
Find LCM of 416,255,282,115,312 with Prime Factorization
| 2 | 416, 255, 282, 115, 312 |
| 2 | 208, 255, 141, 115, 156 |
| 2 | 104, 255, 141, 115, 78 |
| 3 | 52, 255, 141, 115, 39 |
| 5 | 52, 85, 47, 115, 13 |
| 13 | 52, 17, 47, 23, 13 |
| 4, 17, 47, 23, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 13 x 4 x 17 x 47 x 23 x 1 = 114672480
Therefore, the lowest common multiple of 416,255,282,115,312 is 114672480.
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.
416 x 255 x 282 x 115 x 312 = 1073334412800
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.
416 : 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
255 : 1, 3, 5, 15, 17, 51, 85, 255
282 : 1, 2, 3, 6, 47, 94, 141, 282
115 : 1, 5, 23, 115
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 416,255,282,115,312, is 1.
Now, the common factors can be found like this.
416:2x 2x 2x 2x 2x 13
255:3x 5x 17
282:2x 3x 47
115:5x 23
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 2x 3x 3x 5x 13 = 9360
Therefore, the value for common factors is 9360.
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 = 1073334412800/(1x9360)
LCM = 1073334412800/9360
LCM = 114672480
Thus, we can understand that the LCM of 416,255,282,115,312 is 114672480.
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FAQs on LCM of 416, 255, 282, 115, 312
1. What is the LCM of 416, 255, 282, 115, 312?
Answer: LCM of 416, 255, 282, 115, 312 is 114672480.
2. How to calculate the LCM of 416, 255, 282, 115, 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 416, 255, 282, 115, 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}.