LCM of 978, 510, 550, 214
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 978, 510, 550, 214 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 978, 510, 550, 214. So, keep reading to learn more.
Given numbers are 978,510,550,214
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 978,510,550,214 is 489220050.
Find LCM of 978,510,550,214 with Prime Factorization
| 2 | 978, 510, 550, 214 |
| 3 | 489, 255, 275, 107 |
| 5 | 163, 85, 275, 107 |
| 163, 17, 55, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 163 x 17 x 55 x 107 = 489220050
Therefore, the lowest common multiple of 978,510,550,214 is 489220050.
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.
978 x 510 x 550 x 214 = 58706406000
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.
978 : 1, 2, 3, 6, 163, 326, 489, 978
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
550 : 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550
214 : 1, 2, 107, 214
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 978,510,550,214, is 2.
Now, the common factors can be found like this.
978:2x 3x 163
510:2x 3x 5x 17
550:2x 5x 5x 11
214:2x 107
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 3x 5 = 60
Therefore, the value for common factors is 60.
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 = 58706406000/(2x60)
LCM = 58706406000/120
LCM = 489220050
Thus, we can understand that the LCM of 978,510,550,214 is 489220050.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 978, 510, 550, 214
1. What is the LCM of 978, 510, 550, 214?
Answer: LCM of 978, 510, 550, 214 is 489220050.
2. How to calculate the LCM of 978, 510, 550, 214?
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 978, 510, 550, 214.
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}.