LCM of 729, 54, 309
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 729, 54, 309 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, 54, 309. So, keep reading to learn more.
Given numbers are 729,54,309
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 729,54,309 is 150174.
Find LCM of 729,54,309 with Prime Factorization
| 3 | 729, 54, 309 |
| 3 | 243, 18, 103 |
| 3 | 81, 6, 103 |
| 27, 2, 103 |
Multiply the prime numbers at the bottom and the left side.
3 x 3 x 3 x 27 x 2 x 103 = 150174
Therefore, the lowest common multiple of 729,54,309 is 150174.
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 54 x 309 = 12164094
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
54 : 1, 2, 3, 6, 9, 18, 27, 54
309 : 1, 3, 103, 309
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 729,54,309, is 3.
Now, the common factors can be found like this.
729:3x 3x 3x 3x 3x 3
54:2x 3x 3x 3
309:3x 103
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 3x 3 = 27
Therefore, the value for common factors is 27.
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 = 12164094/(3x27)
LCM = 12164094/81
LCM = 150174
Thus, we can understand that the LCM of 729,54,309 is 150174.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 729, 54, 309
1. What is the LCM of 729, 54, 309?
Answer: LCM of 729, 54, 309 is 150174.
2. How to calculate the LCM of 729, 54, 309?
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, 54, 309.
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}.