LCM of 216, 309, 642, 192
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 216, 309, 642, 192 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 216, 309, 642, 192. So, keep reading to learn more.
Given numbers are 216,309,642,192
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 216,309,642,192 is 19044288.
Find LCM of 216,309,642,192 with Prime Factorization
| 2 | 216, 309, 642, 192 |
| 2 | 108, 309, 321, 96 |
| 2 | 54, 309, 321, 48 |
| 3 | 27, 309, 321, 24 |
| 9, 103, 107, 8 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 9 x 103 x 107 x 8 = 19044288
Therefore, the lowest common multiple of 216,309,642,192 is 19044288.
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.
216 x 309 x 642 x 192 = 8227132416
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.
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
309 : 1, 3, 103, 309
642 : 1, 2, 3, 6, 107, 214, 321, 642
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 216,309,642,192, is 3.
Now, the common factors can be found like this.
216:2x 2x 2x 3x 3x 3
309:3x 103
642:2x 3x 107
192:2x 2x 2x 2x 2x 2x 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 3 = 144
Therefore, the value for common factors is 144.
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 = 8227132416/(3x144)
LCM = 8227132416/432
LCM = 19044288
Thus, we can understand that the LCM of 216,309,642,192 is 19044288.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 216, 309, 642, 192
1. What is the LCM of 216, 309, 642, 192?
Answer: LCM of 216, 309, 642, 192 is 19044288.
2. How to calculate the LCM of 216, 309, 642, 192?
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 216, 309, 642, 192.
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}.