LCM of 238, 270, 345, 289
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 238, 270, 345, 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 238, 270, 345, 289. So, keep reading to learn more.
Given numbers are 238,270,345,289
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 238,270,345,289 is 12562830.
Find LCM of 238,270,345,289 with Prime Factorization
| 2 | 238, 270, 345, 289 |
| 3 | 119, 135, 345, 289 |
| 5 | 119, 45, 115, 289 |
| 17 | 119, 9, 23, 289 |
| 7, 9, 23, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 17 x 7 x 9 x 23 x 17 = 12562830
Therefore, the lowest common multiple of 238,270,345,289 is 12562830.
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.
238 x 270 x 345 x 289 = 6407043300
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.
238 : 1, 2, 7, 14, 17, 34, 119, 238
270 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
345 : 1, 3, 5, 15, 23, 69, 115, 345
289 : 1, 17, 289
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 238,270,345,289, is 1.
Now, the common factors can be found like this.
238:2x 7x 17
270:2x 3x 3x 3x 5
345:3x 5x 23
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 3x 5x 17 = 510
Therefore, the value for common factors is 510.
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 = 6407043300/(1x510)
LCM = 6407043300/510
LCM = 12562830
Thus, we can understand that the LCM of 238,270,345,289 is 12562830.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 238, 270, 345, 289
1. What is the LCM of 238, 270, 345, 289?
Answer: LCM of 238, 270, 345, 289 is 12562830.
2. How to calculate the LCM of 238, 270, 345, 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 238, 270, 345, 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}.