LCM of 126, 192, 678, 960
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 126, 192, 678, 960 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 126, 192, 678, 960. So, keep reading to learn more.
Given numbers are 126,192,678,960
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 126,192,678,960 is 2278080.
Find LCM of 126,192,678,960 with Prime Factorization
| 2 | 126, 192, 678, 960 |
| 2 | 63, 96, 339, 480 |
| 2 | 63, 48, 339, 240 |
| 2 | 63, 24, 339, 120 |
| 2 | 63, 12, 339, 60 |
| 2 | 63, 6, 339, 30 |
| 3 | 63, 3, 339, 15 |
| 21, 1, 113, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 2 x 3 x 21 x 1 x 113 x 5 = 2278080
Therefore, the lowest common multiple of 126,192,678,960 is 2278080.
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.
126 x 192 x 678 x 960 = 15746088960
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.
126 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
678 : 1, 2, 3, 6, 113, 226, 339, 678
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 126,192,678,960, is 6.
Now, the common factors can be found like this.
126:2x 3x 3x 7
192:2x 2x 2x 2x 2x 2x 3
678:2x 3x 113
960:2x 2x 2x 2x 2x 2x 3x 5
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 2x 2x 2x 3x 3 = 1152
Therefore, the value for common factors is 1152.
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 = 15746088960/(6x1152)
LCM = 15746088960/6912
LCM = 2278080
Thus, we can understand that the LCM of 126,192,678,960 is 2278080.
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FAQs on LCM of 126, 192, 678, 960
1. What is the LCM of 126, 192, 678, 960?
Answer: LCM of 126, 192, 678, 960 is 2278080.
2. How to calculate the LCM of 126, 192, 678, 960?
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 126, 192, 678, 960.
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}.