LCM of 614, 420, 456, 828, 642
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 614, 420, 456, 828, 642 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 614, 420, 456, 828, 642. So, keep reading to learn more.
Given numbers are 614,420,456,828,642
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 614,420,456,828,642 is 36174632760.
Find LCM of 614,420,456,828,642 with Prime Factorization
| 2 | 614, 420, 456, 828, 642 |
| 2 | 307, 210, 228, 414, 321 |
| 3 | 307, 105, 114, 207, 321 |
| 307, 35, 38, 69, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 307 x 35 x 38 x 69 x 107 = 36174632760
Therefore, the lowest common multiple of 614,420,456,828,642 is 36174632760.
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.
614 x 420 x 456 x 828 x 642 = 62509765409280
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.
614 : 1, 2, 307, 614
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
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
828 : 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
642 : 1, 2, 3, 6, 107, 214, 321, 642
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 614,420,456,828,642, is 2.
Now, the common factors can be found like this.
614:2x 307
420:2x 2x 3x 5x 7
456:2x 2x 2x 3x 19
828:2x 2x 3x 3x 23
642:2x 3x 107
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 3x 3x 3 = 864
Therefore, the value for common factors is 864.
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 = 62509765409280/(2x864)
LCM = 62509765409280/1728
LCM = 36174632760
Thus, we can understand that the LCM of 614,420,456,828,642 is 36174632760.
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FAQs on LCM of 614, 420, 456, 828, 642
1. What is the LCM of 614, 420, 456, 828, 642?
Answer: LCM of 614, 420, 456, 828, 642 is 36174632760.
2. How to calculate the LCM of 614, 420, 456, 828, 642?
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 614, 420, 456, 828, 642.
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}.