LCM of 309, 756, 648, 816
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 309, 756, 648, 816 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 309, 756, 648, 816. So, keep reading to learn more.
Given numbers are 309,756,648,816
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 309,756,648,816 is 15885072.
Find LCM of 309,756,648,816 with Prime Factorization
| 2 | 309, 756, 648, 816 |
| 2 | 309, 378, 324, 408 |
| 2 | 309, 189, 162, 204 |
| 3 | 309, 189, 81, 102 |
| 3 | 103, 63, 27, 34 |
| 3 | 103, 21, 9, 34 |
| 103, 7, 3, 34 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 3 x 103 x 7 x 3 x 34 = 15885072
Therefore, the lowest common multiple of 309,756,648,816 is 15885072.
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.
309 x 756 x 648 x 816 = 123522319872
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.
309 : 1, 3, 103, 309
756 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
648 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
816 : 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 309,756,648,816, is 3.
Now, the common factors can be found like this.
309:3x 103
756:2x 2x 3x 3x 3x 7
648:2x 2x 2x 3x 3x 3x 3
816:2x 2x 2x 2x 3x 17
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 2x 3x 3x 3x 3 = 2592
Therefore, the value for common factors is 2592.
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 = 123522319872/(3x2592)
LCM = 123522319872/7776
LCM = 15885072
Thus, we can understand that the LCM of 309,756,648,816 is 15885072.
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FAQs on LCM of 309, 756, 648, 816
1. What is the LCM of 309, 756, 648, 816?
Answer: LCM of 309, 756, 648, 816 is 15885072.
2. How to calculate the LCM of 309, 756, 648, 816?
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 309, 756, 648, 816.
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}.