LCM of 378, 694, 420, 614
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 378, 694, 420, 614 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 378, 694, 420, 614. So, keep reading to learn more.
Given numbers are 378,694,420,614
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 378,694,420,614 is 402679620.
Find LCM of 378,694,420,614 with Prime Factorization
| 2 | 378, 694, 420, 614 |
| 3 | 189, 347, 210, 307 |
| 7 | 63, 347, 70, 307 |
| 9, 347, 10, 307 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 7 x 9 x 347 x 10 x 307 = 402679620
Therefore, the lowest common multiple of 378,694,420,614 is 402679620.
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.
378 x 694 x 420 x 614 = 67650176160
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.
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
694 : 1, 2, 347, 694
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
614 : 1, 2, 307, 614
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 378,694,420,614, is 2.
Now, the common factors can be found like this.
378:2x 3x 3x 3x 7
694:2x 347
420:2x 2x 3x 5x 7
614:2x 307
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 7 = 84
Therefore, the value for common factors is 84.
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 = 67650176160/(2x84)
LCM = 67650176160/168
LCM = 402679620
Thus, we can understand that the LCM of 378,694,420,614 is 402679620.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 378, 694, 420, 614
1. What is the LCM of 378, 694, 420, 614?
Answer: LCM of 378, 694, 420, 614 is 402679620.
2. How to calculate the LCM of 378, 694, 420, 614?
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 378, 694, 420, 614.
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}.