LCM of 135, 105, 996, 309
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 135, 105, 996, 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 135, 105, 996, 309. So, keep reading to learn more.
Given numbers are 135,105,996,309
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 135,105,996,309 is 32315220.
Find LCM of 135,105,996,309 with Prime Factorization
| 3 | 135, 105, 996, 309 |
| 5 | 45, 35, 332, 103 |
| 9, 7, 332, 103 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 9 x 7 x 332 x 103 = 32315220
Therefore, the lowest common multiple of 135,105,996,309 is 32315220.
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.
135 x 105 x 996 x 309 = 4362554700
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.
135 : 1, 3, 5, 9, 15, 27, 45, 135
105 : 1, 3, 5, 7, 15, 21, 35, 105
996 : 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996
309 : 1, 3, 103, 309
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 135,105,996,309, is 3.
Now, the common factors can be found like this.
135:3x 3x 3x 5
105:3x 5x 7
996:2x 2x 3x 83
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 5 = 45
Therefore, the value for common factors is 45.
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 = 4362554700/(3x45)
LCM = 4362554700/135
LCM = 32315220
Thus, we can understand that the LCM of 135,105,996,309 is 32315220.
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FAQs on LCM of 135, 105, 996, 309
1. What is the LCM of 135, 105, 996, 309?
Answer: LCM of 135, 105, 996, 309 is 32315220.
2. How to calculate the LCM of 135, 105, 996, 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 135, 105, 996, 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}.