LCM of 378, 504, 144, 729
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 378, 504, 144, 729 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 378, 504, 144, 729. So, keep reading to learn more.
Given numbers are 378,504,144,729
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 378,504,144,729 is 81648.
Find LCM of 378,504,144,729 with Prime Factorization
| 2 | 378, 504, 144, 729 |
| 2 | 189, 252, 72, 729 |
| 2 | 189, 126, 36, 729 |
| 3 | 189, 63, 18, 729 |
| 3 | 21, 63, 6, 243 |
| 3 | 7, 21, 2, 81 |
| 7 | 7, 7, 2, 27 |
| 1, 1, 2, 27 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 3 x 7 x 1 x 1 x 2 x 27 = 81648
Therefore, the lowest common multiple of 378,504,144,729 is 81648.
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.
378 x 504 x 144 x 729 = 19999187712
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.
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
504 : 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
729 : 1, 3, 9, 27, 81, 243, 729
9 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 378,504,144,729, is 9.
Now, the common factors can be found like this.
378:2x 3x 3x 3x 7
504:2x 2x 2x 3x 3x 7
144:2x 2x 2x 2x 3x 3
729:3x 3x 3x 3x 3x 3
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 3x 3x 7 = 27216
Therefore, the value for common factors is 27216.
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 = 19999187712/(9x27216)
LCM = 19999187712/244944
LCM = 81648
Thus, we can understand that the LCM of 378,504,144,729 is 81648.
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FAQs on LCM of 378, 504, 144, 729
1. What is the LCM of 378, 504, 144, 729?
Answer: LCM of 378, 504, 144, 729 is 81648.
2. How to calculate the LCM of 378, 504, 144, 729?
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 378, 504, 144, 729.
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}.