LCM of 546, 378, 728
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 546, 378, 728 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, 378, 728. So, keep reading to learn more.
Given numbers are 546,378,728
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 546,378,728 is 19656.
Find LCM of 546,378,728 with Prime Factorization
| 2 | 546, 378, 728 |
| 3 | 273, 189, 364 |
| 7 | 91, 63, 364 |
| 13 | 13, 9, 52 |
| 1, 9, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 7 x 13 x 1 x 9 x 4 = 19656
Therefore, the lowest common multiple of 546,378,728 is 19656.
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 378 x 728 = 150250464
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
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
14 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 546,378,728, is 14.
Now, the common factors can be found like this.
546:2x 3x 7x 13
378:2x 3x 3x 3x 7
728:2x 2x 2x 7x 13
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 7x 13 = 546
Therefore, the value for common factors is 546.
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 = 150250464/(14x546)
LCM = 150250464/7644
LCM = 19656
Thus, we can understand that the LCM of 546,378,728 is 19656.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 546, 378, 728
1. What is the LCM of 546, 378, 728?
Answer: LCM of 546, 378, 728 is 19656.
2. How to calculate the LCM of 546, 378, 728?
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, 378, 728.
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}.