LCM of 828, 105, 990, 192, 762
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 828, 105, 990, 192, 762 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, 990, 192, 762. So, keep reading to learn more.
Given numbers are 828,105,990,192,762
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 828,105,990,192,762 is 647760960.
Find LCM of 828,105,990,192,762 with Prime Factorization
| 2 | 828, 105, 990, 192, 762 |
| 2 | 414, 105, 495, 96, 381 |
| 3 | 207, 105, 495, 48, 381 |
| 3 | 69, 35, 165, 16, 127 |
| 5 | 23, 35, 55, 16, 127 |
| 23, 7, 11, 16, 127 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 23 x 7 x 11 x 16 x 127 = 647760960
Therefore, the lowest common multiple of 828,105,990,192,762 is 647760960.
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 990 x 192 x 762 = 12592473062400
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
990 : 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
762 : 1, 2, 3, 6, 127, 254, 381, 762
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 828,105,990,192,762, is 3.
Now, the common factors can be found like this.
828:2x 2x 3x 3x 23
105:3x 5x 7
990:2x 3x 3x 5x 11
192:2x 2x 2x 2x 2x 2x 3
762:2x 3x 127
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 3x 3x 5 = 6480
Therefore, the value for common factors is 6480.
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 = 12592473062400/(3x6480)
LCM = 12592473062400/19440
LCM = 647760960
Thus, we can understand that the LCM of 828,105,990,192,762 is 647760960.
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FAQs on LCM of 828, 105, 990, 192, 762
1. What is the LCM of 828, 105, 990, 192, 762?
Answer: LCM of 828, 105, 990, 192, 762 is 647760960.
2. How to calculate the LCM of 828, 105, 990, 192, 762?
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, 990, 192, 762.
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}.