LCM of 784, 724, 420, 396
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 784, 724, 420, 396 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, 724, 420, 396. So, keep reading to learn more.
Given numbers are 784,724,420,396
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 784,724,420,396 is 70242480.
Find LCM of 784,724,420,396 with Prime Factorization
| 2 | 784, 724, 420, 396 |
| 2 | 392, 362, 210, 198 |
| 3 | 196, 181, 105, 99 |
| 7 | 196, 181, 35, 33 |
| 28, 181, 5, 33 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 28 x 181 x 5 x 33 = 70242480
Therefore, the lowest common multiple of 784,724,420,396 is 70242480.
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 724 x 420 x 396 = 94405893120
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
724 : 1, 2, 4, 181, 362, 724
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
396 : 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 784,724,420,396, is 4.
Now, the common factors can be found like this.
784:2x 2x 2x 2x 7x 7
724:2x 2x 181
420:2x 2x 3x 5x 7
396:2x 2x 3x 3x 11
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 3x 7 = 336
Therefore, the value for common factors is 336.
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 = 94405893120/(4x336)
LCM = 94405893120/1344
LCM = 70242480
Thus, we can understand that the LCM of 784,724,420,396 is 70242480.
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FAQs on LCM of 784, 724, 420, 396
1. What is the LCM of 784, 724, 420, 396?
Answer: LCM of 784, 724, 420, 396 is 70242480.
2. How to calculate the LCM of 784, 724, 420, 396?
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, 724, 420, 396.
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}.