LCM of 678, 386, 920, 946, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 386, 920, 946, 420 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, 386, 920, 946, 420. So, keep reading to learn more.
Given numbers are 678,386,920,946,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,386,920,946,420 is 199298493240.
Find LCM of 678,386,920,946,420 with Prime Factorization
| 2 | 678, 386, 920, 946, 420 |
| 2 | 339, 193, 460, 473, 210 |
| 3 | 339, 193, 230, 473, 105 |
| 5 | 113, 193, 230, 473, 35 |
| 113, 193, 46, 473, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 113 x 193 x 46 x 473 x 7 = 199298493240
Therefore, the lowest common multiple of 678,386,920,946,420 is 199298493240.
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 386 x 920 x 946 x 420 = 95663276755200
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
386 : 1, 2, 193, 386
920 : 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
946 : 1, 2, 11, 22, 43, 86, 473, 946
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
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,386,920,946,420, is 2.
Now, the common factors can be found like this.
678:2x 3x 113
386:2x 193
920:2x 2x 2x 5x 23
946:2x 11x 43
420:2x 2x 3x 5x 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 5 = 240
Therefore, the value for common factors is 240.
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 = 95663276755200/(2x240)
LCM = 95663276755200/480
LCM = 199298493240
Thus, we can understand that the LCM of 678,386,920,946,420 is 199298493240.
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FAQs on LCM of 678, 386, 920, 946, 420
1. What is the LCM of 678, 386, 920, 946, 420?
Answer: LCM of 678, 386, 920, 946, 420 is 199298493240.
2. How to calculate the LCM of 678, 386, 920, 946, 420?
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, 386, 920, 946, 420.
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}.