LCM of 868, 678, 546, 460, 442
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 868, 678, 546, 460, 442 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 868, 678, 546, 460, 442. So, keep reading to learn more.
Given numbers are 868,678,546,460,442
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 868,678,546,460,442 is 7478414580.
Find LCM of 868,678,546,460,442 with Prime Factorization
| 2 | 868, 678, 546, 460, 442 |
| 2 | 434, 339, 273, 230, 221 |
| 3 | 217, 339, 273, 115, 221 |
| 7 | 217, 113, 91, 115, 221 |
| 13 | 31, 113, 13, 115, 221 |
| 31, 113, 1, 115, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 13 x 31 x 113 x 1 x 115 x 17 = 7478414580
Therefore, the lowest common multiple of 868,678,546,460,442 is 7478414580.
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.
868 x 678 x 546 x 460 x 442 = 65331429770880
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.
868 : 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868
678 : 1, 2, 3, 6, 113, 226, 339, 678
546 : 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
442 : 1, 2, 13, 17, 26, 34, 221, 442
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 868,678,546,460,442, is 2.
Now, the common factors can be found like this.
868:2x 2x 7x 31
678:2x 3x 113
546:2x 3x 7x 13
460:2x 2x 5x 23
442:2x 13x 17
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 7x 13 = 4368
Therefore, the value for common factors is 4368.
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 = 65331429770880/(2x4368)
LCM = 65331429770880/8736
LCM = 7478414580
Thus, we can understand that the LCM of 868,678,546,460,442 is 7478414580.
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FAQs on LCM of 868, 678, 546, 460, 442
1. What is the LCM of 868, 678, 546, 460, 442?
Answer: LCM of 868, 678, 546, 460, 442 is 7478414580.
2. How to calculate the LCM of 868, 678, 546, 460, 442?
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 868, 678, 546, 460, 442.
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}.