LCM of 789, 217, 312, 315, 978
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 789, 217, 312, 315, 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 789, 217, 312, 315, 978. So, keep reading to learn more.
Given numbers are 789,217,312,315,978
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 789,217,312,315,978 is 43536041640.
Find LCM of 789,217,312,315,978 with Prime Factorization
| 2 | 789, 217, 312, 315, 978 |
| 3 | 789, 217, 156, 315, 489 |
| 7 | 263, 217, 52, 105, 163 |
| 263, 31, 52, 15, 163 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 7 x 263 x 31 x 52 x 15 x 163 = 43536041640
Therefore, the lowest common multiple of 789,217,312,315,978 is 43536041640.
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.
789 x 217 x 312 x 315 x 978 = 16456623739920
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.
789 : 1, 3, 263, 789
217 : 1, 7, 31, 217
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
978 : 1, 2, 3, 6, 163, 326, 489, 978
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 789,217,312,315,978, is 1.
Now, the common factors can be found like this.
789:3x 263
217:7x 31
312:2x 2x 2x 3x 13
315:3x 3x 5x 7
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 3x 3x 3x 7 = 378
Therefore, the value for common factors is 378.
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 = 16456623739920/(1x378)
LCM = 16456623739920/378
LCM = 43536041640
Thus, we can understand that the LCM of 789,217,312,315,978 is 43536041640.
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FAQs on LCM of 789, 217, 312, 315, 978
1. What is the LCM of 789, 217, 312, 315, 978?
Answer: LCM of 789, 217, 312, 315, 978 is 43536041640.
2. How to calculate the LCM of 789, 217, 312, 315, 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 789, 217, 312, 315, 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}.