LCM of 289, 468, 540, 546
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 289, 468, 540, 546 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 289, 468, 540, 546. So, keep reading to learn more.
Given numbers are 289,468,540,546
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 289,468,540,546 is 14201460.
Find LCM of 289,468,540,546 with Prime Factorization
| 2 | 289, 468, 540, 546 |
| 2 | 289, 234, 270, 273 |
| 3 | 289, 117, 135, 273 |
| 3 | 289, 39, 45, 91 |
| 13 | 289, 13, 15, 91 |
| 289, 1, 15, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 13 x 289 x 1 x 15 x 7 = 14201460
Therefore, the lowest common multiple of 289,468,540,546 is 14201460.
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.
289 x 468 x 540 x 546 = 39877699680
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.
289 : 1, 17, 289
468 : 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
546 : 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 289,468,540,546, is 1.
Now, the common factors can be found like this.
289:17x 17
468:2x 2x 3x 3x 13
540:2x 2x 3x 3x 3x 5
546:2x 3x 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 2x 2x 3x 3x 3x 13 = 2808
Therefore, the value for common factors is 2808.
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 = 39877699680/(1x2808)
LCM = 39877699680/2808
LCM = 14201460
Thus, we can understand that the LCM of 289,468,540,546 is 14201460.
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FAQs on LCM of 289, 468, 540, 546
1. What is the LCM of 289, 468, 540, 546?
Answer: LCM of 289, 468, 540, 546 is 14201460.
2. How to calculate the LCM of 289, 468, 540, 546?
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 289, 468, 540, 546.
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}.