LCM of 735, 470, 405, 920, 896
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 735, 470, 405, 920, 896 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 735, 470, 405, 920, 896. So, keep reading to learn more.
Given numbers are 735,470,405,920,896
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 735,470,405,920,896 is 2745912960.
Find LCM of 735,470,405,920,896 with Prime Factorization
| 2 | 735, 470, 405, 920, 896 |
| 2 | 735, 235, 405, 460, 448 |
| 2 | 735, 235, 405, 230, 224 |
| 3 | 735, 235, 405, 115, 112 |
| 5 | 245, 235, 135, 115, 112 |
| 7 | 49, 47, 27, 23, 112 |
| 7, 47, 27, 23, 16 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 7 x 47 x 27 x 23 x 16 = 2745912960
Therefore, the lowest common multiple of 735,470,405,920,896 is 2745912960.
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.
735 x 470 x 405 x 920 x 896 = 115328344320000
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.
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
470 : 1, 2, 5, 10, 47, 94, 235, 470
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
920 : 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
896 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 735,470,405,920,896, is 1.
Now, the common factors can be found like this.
735:3x 5x 7x 7
470:2x 5x 47
405:3x 3x 3x 3x 5
920:2x 2x 2x 5x 23
896:2x 2x 2x 2x 2x 2x 2x 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 2x 2x 3x 5x 5x 5x 7 = 42000
Therefore, the value for common factors is 42000.
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 = 115328344320000/(1x42000)
LCM = 115328344320000/42000
LCM = 2745912960
Thus, we can understand that the LCM of 735,470,405,920,896 is 2745912960.
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FAQs on LCM of 735, 470, 405, 920, 896
1. What is the LCM of 735, 470, 405, 920, 896?
Answer: LCM of 735, 470, 405, 920, 896 is 2745912960.
2. How to calculate the LCM of 735, 470, 405, 920, 896?
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 735, 470, 405, 920, 896.
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}.