LCM of 390, 456, 578, 960
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 390, 456, 578, 960 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, 456, 578, 960. So, keep reading to learn more.
Given numbers are 390,456,578,960
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 390,456,578,960 is 68527680.
Find LCM of 390,456,578,960 with Prime Factorization
| 2 | 390, 456, 578, 960 |
| 2 | 195, 228, 289, 480 |
| 2 | 195, 114, 289, 240 |
| 3 | 195, 57, 289, 120 |
| 5 | 65, 19, 289, 40 |
| 13, 19, 289, 8 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 13 x 19 x 289 x 8 = 68527680
Therefore, the lowest common multiple of 390,456,578,960 is 68527680.
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 456 x 578 x 960 = 98679859200
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
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
578 : 1, 2, 17, 34, 289, 578
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 390,456,578,960, is 2.
Now, the common factors can be found like this.
390:2x 3x 5x 13
456:2x 2x 2x 3x 19
578:2x 17x 17
960:2x 2x 2x 2x 2x 2x 3x 5
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 3x 5 = 720
Therefore, the value for common factors is 720.
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 = 98679859200/(2x720)
LCM = 98679859200/1440
LCM = 68527680
Thus, we can understand that the LCM of 390,456,578,960 is 68527680.
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FAQs on LCM of 390, 456, 578, 960
1. What is the LCM of 390, 456, 578, 960?
Answer: LCM of 390, 456, 578, 960 is 68527680.
2. How to calculate the LCM of 390, 456, 578, 960?
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, 456, 578, 960.
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}.