LCM of 390, 288, 540, 309
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 390, 288, 540, 309 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 390, 288, 540, 309. So, keep reading to learn more.
Given numbers are 390,288,540,309
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 390,288,540,309 is 5784480.
Find LCM of 390,288,540,309 with Prime Factorization
| 2 | 390, 288, 540, 309 |
| 2 | 195, 144, 270, 309 |
| 3 | 195, 72, 135, 309 |
| 3 | 65, 24, 45, 103 |
| 5 | 65, 8, 15, 103 |
| 13, 8, 3, 103 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 13 x 8 x 3 x 103 = 5784480
Therefore, the lowest common multiple of 390,288,540,309 is 5784480.
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.
390 x 288 x 540 x 309 = 18741715200
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.
390 : 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
309 : 1, 3, 103, 309
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 390,288,540,309, is 3.
Now, the common factors can be found like this.
390:2x 3x 5x 13
288:2x 2x 2x 2x 2x 3x 3
540:2x 2x 3x 3x 3x 5
309:3x 103
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 3x 3x 5 = 1080
Therefore, the value for common factors is 1080.
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 = 18741715200/(3x1080)
LCM = 18741715200/3240
LCM = 5784480
Thus, we can understand that the LCM of 390,288,540,309 is 5784480.
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FAQs on LCM of 390, 288, 540, 309
1. What is the LCM of 390, 288, 540, 309?
Answer: LCM of 390, 288, 540, 309 is 5784480.
2. How to calculate the LCM of 390, 288, 540, 309?
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 390, 288, 540, 309.
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}.