LCM of 687, 414, 260, 120, 916
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 687, 414, 260, 120, 916 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 687, 414, 260, 120, 916. So, keep reading to learn more.
Given numbers are 687,414,260,120,916
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 687,414,260,120,916 is 24649560.
Find LCM of 687,414,260,120,916 with Prime Factorization
| 2 | 687, 414, 260, 120, 916 |
| 2 | 687, 207, 130, 60, 458 |
| 3 | 687, 207, 65, 30, 229 |
| 5 | 229, 69, 65, 10, 229 |
| 229 | 229, 69, 13, 2, 229 |
| 1, 69, 13, 2, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 229 x 1 x 69 x 13 x 2 x 1 = 24649560
Therefore, the lowest common multiple of 687,414,260,120,916 is 24649560.
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.
687 x 414 x 260 x 120 x 916 = 8128438905600
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.
687 : 1, 3, 229, 687
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
260 : 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
916 : 1, 2, 4, 229, 458, 916
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 687,414,260,120,916, is 1.
Now, the common factors can be found like this.
687:3x 229
414:2x 3x 3x 23
260:2x 2x 5x 13
120:2x 2x 2x 3x 5
916:2x 2x 229
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 2x 3x 3x 5x 229 = 329760
Therefore, the value for common factors is 329760.
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 = 8128438905600/(1x329760)
LCM = 8128438905600/329760
LCM = 24649560
Thus, we can understand that the LCM of 687,414,260,120,916 is 24649560.
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FAQs on LCM of 687, 414, 260, 120, 916
1. What is the LCM of 687, 414, 260, 120, 916?
Answer: LCM of 687, 414, 260, 120, 916 is 24649560.
2. How to calculate the LCM of 687, 414, 260, 120, 916?
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 687, 414, 260, 120, 916.
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}.