LCM of 309, 204, 115, 728, 196
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 309, 204, 115, 728, 196 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, 204, 115, 728, 196. So, keep reading to learn more.
Given numbers are 309,204,115,728,196
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 309,204,115,728,196 is 3078468120.
Find LCM of 309,204,115,728,196 with Prime Factorization
| 2 | 309, 204, 115, 728, 196 |
| 2 | 309, 102, 115, 364, 98 |
| 3 | 309, 51, 115, 182, 49 |
| 7 | 103, 17, 115, 182, 49 |
| 103, 17, 115, 26, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 103 x 17 x 115 x 26 x 7 = 3078468120
Therefore, the lowest common multiple of 309,204,115,728,196 is 3078468120.
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 204 x 115 x 728 x 196 = 1034365288320
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
204 : 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
115 : 1, 5, 23, 115
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
196 : 1, 2, 4, 7, 14, 28, 49, 98, 196
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 309,204,115,728,196, is 1.
Now, the common factors can be found like this.
309:3x 103
204:2x 2x 3x 17
115:5x 23
728:2x 2x 2x 7x 13
196:2x 2x 7x 7
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 7 = 336
Therefore, the value for common factors is 336.
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 = 1034365288320/(1x336)
LCM = 1034365288320/336
LCM = 3078468120
Thus, we can understand that the LCM of 309,204,115,728,196 is 3078468120.
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FAQs on LCM of 309, 204, 115, 728, 196
1. What is the LCM of 309, 204, 115, 728, 196?
Answer: LCM of 309, 204, 115, 728, 196 is 3078468120.
2. How to calculate the LCM of 309, 204, 115, 728, 196?
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, 204, 115, 728, 196.
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}.