LCM of 504, 714, 784
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 504, 714, 784 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 504, 714, 784. So, keep reading to learn more.
Given numbers are 504,714,784
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 504,714,784 is 119952.
Find LCM of 504,714,784 with Prime Factorization
| 2 | 504, 714, 784 |
| 2 | 252, 357, 392 |
| 2 | 126, 357, 196 |
| 3 | 63, 357, 98 |
| 7 | 21, 119, 98 |
| 3, 17, 14 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 7 x 3 x 17 x 14 = 119952
Therefore, the lowest common multiple of 504,714,784 is 119952.
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.
504 x 714 x 784 = 282127104
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.
504 : 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
714 : 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
14 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 504,714,784, is 14.
Now, the common factors can be found like this.
504:2x 2x 2x 3x 3x 7
714:2x 3x 7x 17
784:2x 2x 2x 2x 7x 7
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 3x 7 = 168
Therefore, the value for common factors is 168.
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 = 282127104/(14x168)
LCM = 282127104/2352
LCM = 119952
Thus, we can understand that the LCM of 504,714,784 is 119952.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 504, 714, 784
1. What is the LCM of 504, 714, 784?
Answer: LCM of 504, 714, 784 is 119952.
2. How to calculate the LCM of 504, 714, 784?
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 504, 714, 784.
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}.