LCM of 675, 345, 198
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 675, 345, 198 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 675, 345, 198. So, keep reading to learn more.
Given numbers are 675,345,198
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 675,345,198 is 341550.
Find LCM of 675,345,198 with Prime Factorization
| 3 | 675, 345, 198 |
| 3 | 225, 115, 66 |
| 5 | 75, 115, 22 |
| 15, 23, 22 |
Multiply the prime numbers at the bottom and the left side.
3 x 3 x 5 x 15 x 23 x 22 = 341550
Therefore, the lowest common multiple of 675,345,198 is 341550.
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.
675 x 345 x 198 = 46109250
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.
675 : 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
345 : 1, 3, 5, 15, 23, 69, 115, 345
198 : 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 675,345,198, is 3.
Now, the common factors can be found like this.
675:3x 3x 3x 5x 5
345:3x 5x 23
198:2x 3x 3x 11
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 = 46109250/(3x45)
LCM = 46109250/135
LCM = 341550
Thus, we can understand that the LCM of 675,345,198 is 341550.
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FAQs on LCM of 675, 345, 198
1. What is the LCM of 675, 345, 198?
Answer: LCM of 675, 345, 198 is 341550.
2. How to calculate the LCM of 675, 345, 198?
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 675, 345, 198.
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}.