LCM of 390, 416, 600, 978
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 390, 416, 600, 978 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, 416, 600, 978. So, keep reading to learn more.
Given numbers are 390,416,600,978
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 390,416,600,978 is 5085600.
Find LCM of 390,416,600,978 with Prime Factorization
| 2 | 390, 416, 600, 978 |
| 2 | 195, 208, 300, 489 |
| 2 | 195, 104, 150, 489 |
| 3 | 195, 52, 75, 489 |
| 5 | 65, 52, 25, 163 |
| 13 | 13, 52, 5, 163 |
| 1, 4, 5, 163 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 13 x 1 x 4 x 5 x 163 = 5085600
Therefore, the lowest common multiple of 390,416,600,978 is 5085600.
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 416 x 600 x 978 = 95202432000
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
416 : 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
600 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
978 : 1, 2, 3, 6, 163, 326, 489, 978
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 390,416,600,978, is 2.
Now, the common factors can be found like this.
390:2x 3x 5x 13
416:2x 2x 2x 2x 2x 13
600:2x 2x 2x 3x 5x 5
978:2x 3x 163
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 5x 13 = 9360
Therefore, the value for common factors is 9360.
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 = 95202432000/(2x9360)
LCM = 95202432000/18720
LCM = 5085600
Thus, we can understand that the LCM of 390,416,600,978 is 5085600.
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FAQs on LCM of 390, 416, 600, 978
1. What is the LCM of 390, 416, 600, 978?
Answer: LCM of 390, 416, 600, 978 is 5085600.
2. How to calculate the LCM of 390, 416, 600, 978?
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, 416, 600, 978.
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}.