LCM of 304, 209, 312, 315
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 304, 209, 312, 315 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 304, 209, 312, 315. So, keep reading to learn more.
Given numbers are 304,209,312,315
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 304,209,312,315 is 13693680.
Find LCM of 304,209,312,315 with Prime Factorization
| 2 | 304, 209, 312, 315 |
| 2 | 152, 209, 156, 315 |
| 2 | 76, 209, 78, 315 |
| 3 | 38, 209, 39, 315 |
| 19 | 38, 209, 13, 105 |
| 2, 11, 13, 105 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 19 x 2 x 11 x 13 x 105 = 13693680
Therefore, the lowest common multiple of 304,209,312,315 is 13693680.
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.
304 x 209 x 312 x 315 = 6244318080
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.
304 : 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
209 : 1, 11, 19, 209
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 304,209,312,315, is 1.
Now, the common factors can be found like this.
304:2x 2x 2x 2x 19
209:11x 19
312:2x 2x 2x 3x 13
315:3x 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 2x 3x 19 = 456
Therefore, the value for common factors is 456.
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 = 6244318080/(1x456)
LCM = 6244318080/456
LCM = 13693680
Thus, we can understand that the LCM of 304,209,312,315 is 13693680.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 304, 209, 312, 315
1. What is the LCM of 304, 209, 312, 315?
Answer: LCM of 304, 209, 312, 315 is 13693680.
2. How to calculate the LCM of 304, 209, 312, 315?
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 304, 209, 312, 315.
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}.