LCM of 315, 364, 507, 260, 505
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 315, 364, 507, 260, 505 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, 364, 507, 260, 505. So, keep reading to learn more.
Given numbers are 315,364,507,260,505
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 315,364,507,260,505 is 21506940.
Find LCM of 315,364,507,260,505 with Prime Factorization
| 2 | 315, 364, 507, 260, 505 |
| 2 | 315, 182, 507, 130, 505 |
| 3 | 315, 91, 507, 65, 505 |
| 5 | 105, 91, 169, 65, 505 |
| 7 | 21, 91, 169, 13, 101 |
| 13 | 3, 13, 169, 13, 101 |
| 3, 1, 1, 13, 101 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 13 x 3 x 1 x 1 x 13 x 101 = 21506940
Therefore, the lowest common multiple of 315,364,507,260,505 is 21506940.
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 364 x 507 x 260 x 505 = 7632813006000
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
364 : 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
507 : 1, 3, 13, 39, 169, 507
260 : 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
505 : 1, 5, 101, 505
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 315,364,507,260,505, is 1.
Now, the common factors can be found like this.
315:3x 3x 5x 7
364:2x 2x 7x 13
507:3x 13x 13
260:2x 2x 5x 13
505:5x 101
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 5x 5x 7x 13x 13 = 354900
Therefore, the value for common factors is 354900.
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 = 7632813006000/(1x354900)
LCM = 7632813006000/354900
LCM = 21506940
Thus, we can understand that the LCM of 315,364,507,260,505 is 21506940.
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FAQs on LCM of 315, 364, 507, 260, 505
1. What is the LCM of 315, 364, 507, 260, 505?
Answer: LCM of 315, 364, 507, 260, 505 is 21506940.
2. How to calculate the LCM of 315, 364, 507, 260, 505?
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, 364, 507, 260, 505.
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}.