LCM of 289, 105, 600, 648
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 289, 105, 600, 648 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, 105, 600, 648. So, keep reading to learn more.
Given numbers are 289,105,600,648
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 289,105,600,648 is 32772600.
Find LCM of 289,105,600,648 with Prime Factorization
| 2 | 289, 105, 600, 648 |
| 2 | 289, 105, 300, 324 |
| 2 | 289, 105, 150, 162 |
| 3 | 289, 105, 75, 81 |
| 5 | 289, 35, 25, 27 |
| 289, 7, 5, 27 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 289 x 7 x 5 x 27 = 32772600
Therefore, the lowest common multiple of 289,105,600,648 is 32772600.
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 105 x 600 x 648 = 11798136000
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
105 : 1, 3, 5, 7, 15, 21, 35, 105
600 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
648 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 289,105,600,648, is 1.
Now, the common factors can be found like this.
289:17x 17
105:3x 5x 7
600:2x 2x 2x 3x 5x 5
648:2x 2x 2x 3x 3x 3x 3
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 5 = 360
Therefore, the value for common factors is 360.
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 = 11798136000/(1x360)
LCM = 11798136000/360
LCM = 32772600
Thus, we can understand that the LCM of 289,105,600,648 is 32772600.
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FAQs on LCM of 289, 105, 600, 648
1. What is the LCM of 289, 105, 600, 648?
Answer: LCM of 289, 105, 600, 648 is 32772600.
2. How to calculate the LCM of 289, 105, 600, 648?
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, 105, 600, 648.
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}.