LCM of 678, 105, 462, 489
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 105, 462, 489 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 678, 105, 462, 489. So, keep reading to learn more.
Given numbers are 678,105,462,489
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,105,462,489 is 42547890.
Find LCM of 678,105,462,489 with Prime Factorization
| 2 | 678, 105, 462, 489 |
| 3 | 339, 105, 231, 489 |
| 7 | 113, 35, 77, 163 |
| 113, 5, 11, 163 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 7 x 113 x 5 x 11 x 163 = 42547890
Therefore, the lowest common multiple of 678,105,462,489 is 42547890.
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.
678 x 105 x 462 x 489 = 16083102420
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.
678 : 1, 2, 3, 6, 113, 226, 339, 678
105 : 1, 3, 5, 7, 15, 21, 35, 105
462 : 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
489 : 1, 3, 163, 489
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,105,462,489, is 3.
Now, the common factors can be found like this.
678:2x 3x 113
105:3x 5x 7
462:2x 3x 7x 11
489:3x 163
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 3x 7 = 126
Therefore, the value for common factors is 126.
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 = 16083102420/(3x126)
LCM = 16083102420/378
LCM = 42547890
Thus, we can understand that the LCM of 678,105,462,489 is 42547890.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 678, 105, 462, 489
1. What is the LCM of 678, 105, 462, 489?
Answer: LCM of 678, 105, 462, 489 is 42547890.
2. How to calculate the LCM of 678, 105, 462, 489?
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 678, 105, 462, 489.
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}.