LCM of 289, 270, 748, 288, 459
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 289, 270, 748, 288, 459 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, 270, 748, 288, 459. So, keep reading to learn more.
Given numbers are 289,270,748,288,459
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 289,270,748,288,459 is 13733280.
Find LCM of 289,270,748,288,459 with Prime Factorization
| 2 | 289, 270, 748, 288, 459 |
| 2 | 289, 135, 374, 144, 459 |
| 3 | 289, 135, 187, 72, 459 |
| 3 | 289, 45, 187, 24, 153 |
| 3 | 289, 15, 187, 8, 51 |
| 17 | 289, 5, 187, 8, 17 |
| 1, 5, 11, 8, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 17 x 1 x 5 x 11 x 8 x 17 = 13733280
Therefore, the lowest common multiple of 289,270,748,288,459 is 13733280.
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 270 x 748 x 288 x 459 = 7715576436480
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
270 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
748 : 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
459 : 1, 3, 9, 17, 27, 51, 153, 459
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 289,270,748,288,459, is 1.
Now, the common factors can be found like this.
289:17x 17
270:2x 3x 3x 3x 5
748:2x 2x 11x 17
288:2x 2x 2x 2x 2x 3x 3
459:3x 3x 3x 17
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 3x 3x 17x 17 = 561816
Therefore, the value for common factors is 561816.
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 = 7715576436480/(1x561816)
LCM = 7715576436480/561816
LCM = 13733280
Thus, we can understand that the LCM of 289,270,748,288,459 is 13733280.
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FAQs on LCM of 289, 270, 748, 288, 459
1. What is the LCM of 289, 270, 748, 288, 459?
Answer: LCM of 289, 270, 748, 288, 459 is 13733280.
2. How to calculate the LCM of 289, 270, 748, 288, 459?
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, 270, 748, 288, 459.
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}.