LCM of 417, 546, 680, 689, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 417, 546, 680, 689, 678 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 417, 546, 680, 689, 678. So, keep reading to learn more.
Given numbers are 417,546,680,689,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 417,546,680,689,678 is 154539916440.
Find LCM of 417,546,680,689,678 with Prime Factorization
| 2 | 417, 546, 680, 689, 678 |
| 3 | 417, 273, 340, 689, 339 |
| 13 | 139, 91, 340, 689, 113 |
| 139, 7, 340, 53, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 13 x 139 x 7 x 340 x 53 x 113 = 154539916440
Therefore, the lowest common multiple of 417,546,680,689,678 is 154539916440.
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.
417 x 546 x 680 x 689 x 678 = 72324680893920
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.
417 : 1, 3, 139, 417
546 : 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
680 : 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
689 : 1, 13, 53, 689
678 : 1, 2, 3, 6, 113, 226, 339, 678
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 417,546,680,689,678, is 1.
Now, the common factors can be found like this.
417:3x 139
546:2x 3x 7x 13
680:2x 2x 2x 5x 17
689:13x 53
678:2x 3x 113
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 3x 13 = 468
Therefore, the value for common factors is 468.
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 = 72324680893920/(1x468)
LCM = 72324680893920/468
LCM = 154539916440
Thus, we can understand that the LCM of 417,546,680,689,678 is 154539916440.
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FAQs on LCM of 417, 546, 680, 689, 678
1. What is the LCM of 417, 546, 680, 689, 678?
Answer: LCM of 417, 546, 680, 689, 678 is 154539916440.
2. How to calculate the LCM of 417, 546, 680, 689, 678?
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 417, 546, 680, 689, 678.
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}.