LCM of 729, 234, 312, 412, 314
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 729, 234, 312, 412, 314 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, 234, 312, 412, 314. So, keep reading to learn more.
Given numbers are 729,234,312,412,314
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 729,234,312,412,314 is 1226020536.
Find LCM of 729,234,312,412,314 with Prime Factorization
| 2 | 729, 234, 312, 412, 314 |
| 2 | 729, 117, 156, 206, 157 |
| 3 | 729, 117, 78, 103, 157 |
| 3 | 243, 39, 26, 103, 157 |
| 13 | 81, 13, 26, 103, 157 |
| 81, 1, 2, 103, 157 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 13 x 81 x 1 x 2 x 103 x 157 = 1226020536
Therefore, the lowest common multiple of 729,234,312,412,314 is 1226020536.
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 234 x 312 x 412 x 314 = 6885331330176
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
234 : 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
412 : 1, 2, 4, 103, 206, 412
314 : 1, 2, 157, 314
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 729,234,312,412,314, is 1.
Now, the common factors can be found like this.
729:3x 3x 3x 3x 3x 3
234:2x 3x 3x 13
312:2x 2x 2x 3x 13
412:2x 2x 103
314:2x 157
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 13 = 5616
Therefore, the value for common factors is 5616.
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 = 6885331330176/(1x5616)
LCM = 6885331330176/5616
LCM = 1226020536
Thus, we can understand that the LCM of 729,234,312,412,314 is 1226020536.
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FAQs on LCM of 729, 234, 312, 412, 314
1. What is the LCM of 729, 234, 312, 412, 314?
Answer: LCM of 729, 234, 312, 412, 314 is 1226020536.
2. How to calculate the LCM of 729, 234, 312, 412, 314?
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, 234, 312, 412, 314.
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}.