LCM of 217, 700, 268, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 217, 700, 268, 414 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 217, 700, 268, 414. So, keep reading to learn more.
Given numbers are 217,700,268,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 217,700,268,414 is 300957300.
Find LCM of 217,700,268,414 with Prime Factorization
| 2 | 217, 700, 268, 414 |
| 2 | 217, 350, 134, 207 |
| 7 | 217, 175, 67, 207 |
| 31, 25, 67, 207 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 7 x 31 x 25 x 67 x 207 = 300957300
Therefore, the lowest common multiple of 217,700,268,414 is 300957300.
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.
217 x 700 x 268 x 414 = 16853608800
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.
217 : 1, 7, 31, 217
700 : 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700
268 : 1, 2, 4, 67, 134, 268
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 217,700,268,414, is 1.
Now, the common factors can be found like this.
217:7x 31
700:2x 2x 5x 5x 7
268:2x 2x 67
414:2x 3x 3x 23
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 7 = 56
Therefore, the value for common factors is 56.
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 = 16853608800/(1x56)
LCM = 16853608800/56
LCM = 300957300
Thus, we can understand that the LCM of 217,700,268,414 is 300957300.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 217, 700, 268, 414
1. What is the LCM of 217, 700, 268, 414?
Answer: LCM of 217, 700, 268, 414 is 300957300.
2. How to calculate the LCM of 217, 700, 268, 414?
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 217, 700, 268, 414.
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}.