LCM of 357, 560, 420, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 357, 560, 420, 105 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 357, 560, 420, 105. So, keep reading to learn more.
Given numbers are 357,560,420,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 357,560,420,105 is 28560.
Find LCM of 357,560,420,105 with Prime Factorization
| 2 | 357, 560, 420, 105 |
| 2 | 357, 280, 210, 105 |
| 3 | 357, 140, 105, 105 |
| 5 | 119, 140, 35, 35 |
| 7 | 119, 28, 7, 7 |
| 17, 4, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 17 x 4 x 1 x 1 = 28560
Therefore, the lowest common multiple of 357,560,420,105 is 28560.
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.
357 x 560 x 420 x 105 = 8816472000
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.
357 : 1, 3, 7, 17, 21, 51, 119, 357
560 : 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
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
105 : 1, 3, 5, 7, 15, 21, 35, 105
7 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 357,560,420,105, is 7.
Now, the common factors can be found like this.
357:3x 7x 17
560:2x 2x 2x 2x 5x 7
420:2x 2x 3x 5x 7
105:3x 5x 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 3x 3x 5x 5x 7x 7 = 44100
Therefore, the value for common factors is 44100.
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 = 8816472000/(7x44100)
LCM = 8816472000/308700
LCM = 28560
Thus, we can understand that the LCM of 357,560,420,105 is 28560.
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FAQs on LCM of 357, 560, 420, 105
1. What is the LCM of 357, 560, 420, 105?
Answer: LCM of 357, 560, 420, 105 is 28560.
2. How to calculate the LCM of 357, 560, 420, 105?
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 357, 560, 420, 105.
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}.