LCM of 546, 675, 135, 690
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 546, 675, 135, 690 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, 675, 135, 690. So, keep reading to learn more.
Given numbers are 546,675,135,690
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 546,675,135,690 is 2825550.
Find LCM of 546,675,135,690 with Prime Factorization
| 2 | 546, 675, 135, 690 |
| 3 | 273, 675, 135, 345 |
| 3 | 91, 225, 45, 115 |
| 3 | 91, 75, 15, 115 |
| 5 | 91, 25, 5, 115 |
| 91, 1, 5, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 3 x 5 x 91 x 1 x 5 x 23 = 2825550
Therefore, the lowest common multiple of 546,675,135,690 is 2825550.
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 675 x 135 x 690 = 34330432500
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
675 : 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
135 : 1, 3, 5, 9, 15, 27, 45, 135
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 546,675,135,690, is 3.
Now, the common factors can be found like this.
546:2x 3x 7x 13
675:3x 3x 3x 5x 5
135:3x 3x 3x 5
690:2x 3x 5x 23
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 3x 3x 3x 5x 5 = 4050
Therefore, the value for common factors is 4050.
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 = 34330432500/(3x4050)
LCM = 34330432500/12150
LCM = 2825550
Thus, we can understand that the LCM of 546,675,135,690 is 2825550.
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FAQs on LCM of 546, 675, 135, 690
1. What is the LCM of 546, 675, 135, 690?
Answer: LCM of 546, 675, 135, 690 is 2825550.
2. How to calculate the LCM of 546, 675, 135, 690?
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, 675, 135, 690.
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}.