LCM of 678, 200, 240, 234, 614
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 200, 240, 234, 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 678, 200, 240, 234, 614. So, keep reading to learn more.
Given numbers are 678,200,240,234,614
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,200,240,234,614 is 1623538800.
Find LCM of 678,200,240,234,614 with Prime Factorization
| 2 | 678, 200, 240, 234, 614 |
| 2 | 339, 100, 120, 117, 307 |
| 2 | 339, 50, 60, 117, 307 |
| 3 | 339, 25, 30, 117, 307 |
| 5 | 113, 25, 10, 39, 307 |
| 113, 5, 2, 39, 307 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 113 x 5 x 2 x 39 x 307 = 1623538800
Therefore, the lowest common multiple of 678,200,240,234,614 is 1623538800.
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 200 x 240 x 234 x 614 = 4675791744000
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
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
234 : 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
614 : 1, 2, 307, 614
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,200,240,234,614, is 2.
Now, the common factors can be found like this.
678:2x 3x 113
200:2x 2x 2x 5x 5
240:2x 2x 2x 2x 3x 5
234:2x 3x 3x 13
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 2x 2x 2x 3x 3x 5 = 1440
Therefore, the value for common factors is 1440.
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 = 4675791744000/(2x1440)
LCM = 4675791744000/2880
LCM = 1623538800
Thus, we can understand that the LCM of 678,200,240,234,614 is 1623538800.
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FAQs on LCM of 678, 200, 240, 234, 614
1. What is the LCM of 678, 200, 240, 234, 614?
Answer: LCM of 678, 200, 240, 234, 614 is 1623538800.
2. How to calculate the LCM of 678, 200, 240, 234, 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 678, 200, 240, 234, 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}.