LCM of 420, 838, 224, 728
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 838, 224, 728 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 420, 838, 224, 728. So, keep reading to learn more.
Given numbers are 420,838,224,728
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,838,224,728 is 18301920.
Find LCM of 420,838,224,728 with Prime Factorization
| 2 | 420, 838, 224, 728 |
| 2 | 210, 419, 112, 364 |
| 2 | 105, 419, 56, 182 |
| 7 | 105, 419, 28, 91 |
| 15, 419, 4, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 7 x 15 x 419 x 4 x 13 = 18301920
Therefore, the lowest common multiple of 420,838,224,728 is 18301920.
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.
420 x 838 x 224 x 728 = 57394821120
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.
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
838 : 1, 2, 419, 838
224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,838,224,728, is 2.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
838:2x 419
224:2x 2x 2x 2x 2x 7
728:2x 2x 2x 7x 13
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 7x 7 = 1568
Therefore, the value for common factors is 1568.
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 = 57394821120/(2x1568)
LCM = 57394821120/3136
LCM = 18301920
Thus, we can understand that the LCM of 420,838,224,728 is 18301920.
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FAQs on LCM of 420, 838, 224, 728
1. What is the LCM of 420, 838, 224, 728?
Answer: LCM of 420, 838, 224, 728 is 18301920.
2. How to calculate the LCM of 420, 838, 224, 728?
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 420, 838, 224, 728.
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}.