LCM of 684, 678, 504, 514, 378
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 684, 678, 504, 514, 378 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 684, 678, 504, 514, 378. So, keep reading to learn more.
Given numbers are 684,678,504,514,378
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 684,678,504,514,378 is 834289848.
Find LCM of 684,678,504,514,378 with Prime Factorization
| 2 | 684, 678, 504, 514, 378 |
| 2 | 342, 339, 252, 257, 189 |
| 3 | 171, 339, 126, 257, 189 |
| 3 | 57, 113, 42, 257, 63 |
| 7 | 19, 113, 14, 257, 21 |
| 19, 113, 2, 257, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 7 x 19 x 113 x 2 x 257 x 3 = 834289848
Therefore, the lowest common multiple of 684,678,504,514,378 is 834289848.
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.
684 x 678 x 504 x 514 x 378 = 45412065006336
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.
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
678 : 1, 2, 3, 6, 113, 226, 339, 678
504 : 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
514 : 1, 2, 257, 514
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 684,678,504,514,378, is 2.
Now, the common factors can be found like this.
684:2x 2x 3x 3x 19
678:2x 3x 113
504:2x 2x 2x 3x 3x 7
514:2x 257
378:2x 3x 3x 3x 7
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 3x 7 = 27216
Therefore, the value for common factors is 27216.
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 = 45412065006336/(2x27216)
LCM = 45412065006336/54432
LCM = 834289848
Thus, we can understand that the LCM of 684,678,504,514,378 is 834289848.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 684, 678, 504, 514, 378
1. What is the LCM of 684, 678, 504, 514, 378?
Answer: LCM of 684, 678, 504, 514, 378 is 834289848.
2. How to calculate the LCM of 684, 678, 504, 514, 378?
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 684, 678, 504, 514, 378.
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}.