LCM of 546, 198, 105, 990
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 546, 198, 105, 990 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 546, 198, 105, 990. So, keep reading to learn more.
Given numbers are 546,198,105,990
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 546,198,105,990 is 90090.
Find LCM of 546,198,105,990 with Prime Factorization
| 2 | 546, 198, 105, 990 |
| 3 | 273, 99, 105, 495 |
| 3 | 91, 33, 35, 165 |
| 5 | 91, 11, 35, 55 |
| 7 | 91, 11, 7, 11 |
| 11 | 13, 11, 1, 11 |
| 13, 1, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 5 x 7 x 11 x 13 x 1 x 1 x 1 = 90090
Therefore, the lowest common multiple of 546,198,105,990 is 90090.
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.
546 x 198 x 105 x 990 = 11237826600
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.
546 : 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
198 : 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
105 : 1, 3, 5, 7, 15, 21, 35, 105
990 : 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 546,198,105,990, is 3.
Now, the common factors can be found like this.
546:2x 3x 7x 13
198:2x 3x 3x 11
105:3x 5x 7
990:2x 3x 3x 5x 11
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 3x 3x 3x 5x 7x 11 = 41580
Therefore, the value for common factors is 41580.
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 = 11237826600/(3x41580)
LCM = 11237826600/124740
LCM = 90090
Thus, we can understand that the LCM of 546,198,105,990 is 90090.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 546, 198, 105, 990
1. What is the LCM of 546, 198, 105, 990?
Answer: LCM of 546, 198, 105, 990 is 90090.
2. How to calculate the LCM of 546, 198, 105, 990?
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 546, 198, 105, 990.
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}.