LCM of 729, 978, 216, 400
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 729, 978, 216, 400 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 729, 978, 216, 400. So, keep reading to learn more.
Given numbers are 729,978,216,400
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 729,978,216,400 is 47530800.
Find LCM of 729,978,216,400 with Prime Factorization
| 2 | 729, 978, 216, 400 |
| 2 | 729, 489, 108, 200 |
| 2 | 729, 489, 54, 100 |
| 3 | 729, 489, 27, 50 |
| 3 | 243, 163, 9, 50 |
| 3 | 81, 163, 3, 50 |
| 27, 163, 1, 50 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 3 x 27 x 163 x 1 x 50 = 47530800
Therefore, the lowest common multiple of 729,978,216,400 is 47530800.
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.
729 x 978 x 216 x 400 = 61599916800
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.
729 : 1, 3, 9, 27, 81, 243, 729
978 : 1, 2, 3, 6, 163, 326, 489, 978
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 729,978,216,400, is 1.
Now, the common factors can be found like this.
729:3x 3x 3x 3x 3x 3
978:2x 3x 163
216:2x 2x 2x 3x 3x 3
400:2x 2x 2x 2x 5x 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 3x 3 = 1296
Therefore, the value for common factors is 1296.
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 = 61599916800/(1x1296)
LCM = 61599916800/1296
LCM = 47530800
Thus, we can understand that the LCM of 729,978,216,400 is 47530800.
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FAQs on LCM of 729, 978, 216, 400
1. What is the LCM of 729, 978, 216, 400?
Answer: LCM of 729, 978, 216, 400 is 47530800.
2. How to calculate the LCM of 729, 978, 216, 400?
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 729, 978, 216, 400.
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}.