LCM of 75, 810, 102
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 75, 810, 102 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 75, 810, 102. So, keep reading to learn more.
Given numbers are 75,810,102
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 75,810,102 is 68850.
Find LCM of 75,810,102 with Prime Factorization
| 2 | 75, 810, 102 |
| 3 | 75, 405, 51 |
| 5 | 25, 135, 17 |
| 5, 27, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 5 x 27 x 17 = 68850
Therefore, the lowest common multiple of 75,810,102 is 68850.
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.
75 x 810 x 102 = 6196500
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.
75 : 1, 3, 5, 15, 25, 75
810 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
102 : 1, 2, 3, 6, 17, 34, 51, 102
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 75,810,102, is 3.
Now, the common factors can be found like this.
75:3x 5x 5
810:2x 3x 3x 3x 3x 5
102:2x 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 3x 5 = 30
Therefore, the value for common factors is 30.
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 = 6196500/(3x30)
LCM = 6196500/90
LCM = 68850
Thus, we can understand that the LCM of 75,810,102 is 68850.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 75, 810, 102
1. What is the LCM of 75, 810, 102?
Answer: LCM of 75, 810, 102 is 68850.
2. How to calculate the LCM of 75, 810, 102?
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 75, 810, 102.
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}.