LCM of 105, 270, 311, 392, 410
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 270, 311, 392, 410 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 105, 270, 311, 392, 410. So, keep reading to learn more.
Given numbers are 105,270,311,392,410
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,270,311,392,410 is 674782920.
Find LCM of 105,270,311,392,410 with Prime Factorization
| 2 | 105, 270, 311, 392, 410 |
| 3 | 105, 135, 311, 196, 205 |
| 5 | 35, 45, 311, 196, 205 |
| 7 | 7, 9, 311, 196, 41 |
| 1, 9, 311, 28, 41 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 1 x 9 x 311 x 28 x 41 = 674782920
Therefore, the lowest common multiple of 105,270,311,392,410 is 674782920.
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.
105 x 270 x 311 x 392 x 410 = 1417044132000
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.
105 : 1, 3, 5, 7, 15, 21, 35, 105
270 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
311 : 1, 311
392 : 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
410 : 1, 2, 5, 10, 41, 82, 205, 410
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,270,311,392,410, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
270:2x 3x 3x 3x 5
311:311
392:2x 2x 2x 7x 7
410:2x 5x 41
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 3x 5x 5x 7 = 2100
Therefore, the value for common factors is 2100.
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 = 1417044132000/(1x2100)
LCM = 1417044132000/2100
LCM = 674782920
Thus, we can understand that the LCM of 105,270,311,392,410 is 674782920.
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FAQs on LCM of 105, 270, 311, 392, 410
1. What is the LCM of 105, 270, 311, 392, 410?
Answer: LCM of 105, 270, 311, 392, 410 is 674782920.
2. How to calculate the LCM of 105, 270, 311, 392, 410?
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 105, 270, 311, 392, 410.
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}.