LCM of 315, 642, 414, 240, 735
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 315, 642, 414, 240, 735 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 315, 642, 414, 240, 735. So, keep reading to learn more.
Given numbers are 315,642,414,240,735
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 315,642,414,240,735 is 86824080.
Find LCM of 315,642,414,240,735 with Prime Factorization
| 2 | 315, 642, 414, 240, 735 |
| 3 | 315, 321, 207, 120, 735 |
| 3 | 105, 107, 69, 40, 245 |
| 5 | 35, 107, 23, 40, 245 |
| 7 | 7, 107, 23, 8, 49 |
| 1, 107, 23, 8, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 5 x 7 x 1 x 107 x 23 x 8 x 7 = 86824080
Therefore, the lowest common multiple of 315,642,414,240,735 is 86824080.
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.
315 x 642 x 414 x 240 x 735 = 14768776008000
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.
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
642 : 1, 2, 3, 6, 107, 214, 321, 642
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 315,642,414,240,735, is 3.
Now, the common factors can be found like this.
315:3x 3x 5x 7
642:2x 3x 107
414:2x 3x 3x 23
240:2x 2x 2x 2x 3x 5
735:3x 5x 7x 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 3x 3x 5x 5x 7 = 56700
Therefore, the value for common factors is 56700.
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 = 14768776008000/(3x56700)
LCM = 14768776008000/170100
LCM = 86824080
Thus, we can understand that the LCM of 315,642,414,240,735 is 86824080.
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FAQs on LCM of 315, 642, 414, 240, 735
1. What is the LCM of 315, 642, 414, 240, 735?
Answer: LCM of 315, 642, 414, 240, 735 is 86824080.
2. How to calculate the LCM of 315, 642, 414, 240, 735?
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 315, 642, 414, 240, 735.
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}.