LCM of 102, 120, 238, 578, 289
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 102, 120, 238, 578, 289 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 102, 120, 238, 578, 289. So, keep reading to learn more.
Given numbers are 102,120,238,578,289
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 102,120,238,578,289 is 242760.
Find LCM of 102,120,238,578,289 with Prime Factorization
| 2 | 102, 120, 238, 578, 289 |
| 3 | 51, 60, 119, 289, 289 |
| 17 | 17, 20, 119, 289, 289 |
| 17 | 1, 20, 7, 17, 17 |
| 1, 20, 7, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 17 x 17 x 1 x 20 x 7 x 1 x 1 = 242760
Therefore, the lowest common multiple of 102,120,238,578,289 is 242760.
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.
102 x 120 x 238 x 578 x 289 = 486613391040
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.
102 : 1, 2, 3, 6, 17, 34, 51, 102
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
238 : 1, 2, 7, 14, 17, 34, 119, 238
578 : 1, 2, 17, 34, 289, 578
289 : 1, 17, 289
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 102,120,238,578,289, is 1.
Now, the common factors can be found like this.
102:2x 3x 17
120:2x 2x 2x 3x 5
238:2x 7x 17
578:2x 17x 17
289:17x 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 17x 17x 17x 17 = 2004504
Therefore, the value for common factors is 2004504.
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 = 486613391040/(1x2004504)
LCM = 486613391040/2004504
LCM = 242760
Thus, we can understand that the LCM of 102,120,238,578,289 is 242760.
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FAQs on LCM of 102, 120, 238, 578, 289
1. What is the LCM of 102, 120, 238, 578, 289?
Answer: LCM of 102, 120, 238, 578, 289 is 242760.
2. How to calculate the LCM of 102, 120, 238, 578, 289?
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 102, 120, 238, 578, 289.
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}.