LCM of 828, 105, 102, 578
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 828, 105, 102, 578 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 828, 105, 102, 578. So, keep reading to learn more.
Given numbers are 828,105,102,578
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 828,105,102,578 is 8375220.
Find LCM of 828,105,102,578 with Prime Factorization
| 2 | 828, 105, 102, 578 |
| 3 | 414, 105, 51, 289 |
| 17 | 138, 35, 17, 289 |
| 138, 35, 1, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 17 x 138 x 35 x 1 x 17 = 8375220
Therefore, the lowest common multiple of 828,105,102,578 is 8375220.
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.
828 x 105 x 102 x 578 = 5125634640
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.
828 : 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
105 : 1, 3, 5, 7, 15, 21, 35, 105
102 : 1, 2, 3, 6, 17, 34, 51, 102
578 : 1, 2, 17, 34, 289, 578
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 828,105,102,578, is 1.
Now, the common factors can be found like this.
828:2x 2x 3x 3x 23
105:3x 5x 7
102:2x 3x 17
578:2x 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 3x 3x 17 = 612
Therefore, the value for common factors is 612.
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 = 5125634640/(1x612)
LCM = 5125634640/612
LCM = 8375220
Thus, we can understand that the LCM of 828,105,102,578 is 8375220.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 828, 105, 102, 578
1. What is the LCM of 828, 105, 102, 578?
Answer: LCM of 828, 105, 102, 578 is 8375220.
2. How to calculate the LCM of 828, 105, 102, 578?
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 828, 105, 102, 578.
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}.