LCM of 428, 144, 240, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 428, 144, 240, 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 428, 144, 240, 414. So, keep reading to learn more.
Given numbers are 428,144,240,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 428,144,240,414 is 1771920.
Find LCM of 428,144,240,414 with Prime Factorization
| 2 | 428, 144, 240, 414 |
| 2 | 214, 72, 120, 207 |
| 2 | 107, 36, 60, 207 |
| 2 | 107, 18, 30, 207 |
| 3 | 107, 9, 15, 207 |
| 3 | 107, 3, 5, 69 |
| 107, 1, 5, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 107 x 1 x 5 x 23 = 1771920
Therefore, the lowest common multiple of 428,144,240,414 is 1771920.
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.
428 x 144 x 240 x 414 = 6123755520
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.
428 : 1, 2, 4, 107, 214, 428
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
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 428,144,240,414, is 2.
Now, the common factors can be found like this.
428:2x 2x 107
144:2x 2x 2x 2x 3x 3
240:2x 2x 2x 2x 3x 5
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 2x 2x 2x 3x 3x 3 = 1728
Therefore, the value for common factors is 1728.
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 = 6123755520/(2x1728)
LCM = 6123755520/3456
LCM = 1771920
Thus, we can understand that the LCM of 428,144,240,414 is 1771920.
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FAQs on LCM of 428, 144, 240, 414
1. What is the LCM of 428, 144, 240, 414?
Answer: LCM of 428, 144, 240, 414 is 1771920.
2. How to calculate the LCM of 428, 144, 240, 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 428, 144, 240, 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}.