LCM of 784, 306, 782, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 784, 306, 782, 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 784, 306, 782, 414. So, keep reading to learn more.
Given numbers are 784,306,782,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 784,306,782,414 is 2758896.
Find LCM of 784,306,782,414 with Prime Factorization
| 2 | 784, 306, 782, 414 |
| 3 | 392, 153, 391, 207 |
| 3 | 392, 51, 391, 69 |
| 17 | 392, 17, 391, 23 |
| 23 | 392, 1, 23, 23 |
| 392, 1, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 17 x 23 x 392 x 1 x 1 x 1 = 2758896
Therefore, the lowest common multiple of 784,306,782,414 is 2758896.
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.
784 x 306 x 782 x 414 = 77668440192
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.
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
782 : 1, 2, 17, 23, 34, 46, 391, 782
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 784,306,782,414, is 2.
Now, the common factors can be found like this.
784:2x 2x 2x 2x 7x 7
306:2x 3x 3x 17
782:2x 17x 23
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 3x 3x 17x 23 = 14076
Therefore, the value for common factors is 14076.
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 = 77668440192/(2x14076)
LCM = 77668440192/28152
LCM = 2758896
Thus, we can understand that the LCM of 784,306,782,414 is 2758896.
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FAQs on LCM of 784, 306, 782, 414
1. What is the LCM of 784, 306, 782, 414?
Answer: LCM of 784, 306, 782, 414 is 2758896.
2. How to calculate the LCM of 784, 306, 782, 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 784, 306, 782, 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}.