LCM of 238, 216, 306, 270
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 238, 216, 306, 270 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, 216, 306, 270. So, keep reading to learn more.
Given numbers are 238,216,306,270
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 238,216,306,270 is 128520.
Find LCM of 238,216,306,270 with Prime Factorization
| 2 | 238, 216, 306, 270 |
| 3 | 119, 108, 153, 135 |
| 3 | 119, 36, 51, 45 |
| 3 | 119, 12, 17, 15 |
| 17 | 119, 4, 17, 5 |
| 7, 4, 1, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 3 x 17 x 7 x 4 x 1 x 5 = 128520
Therefore, the lowest common multiple of 238,216,306,270 is 128520.
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 216 x 306 x 270 = 4247328960
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
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
270 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 238,216,306,270, is 2.
Now, the common factors can be found like this.
238:2x 7x 17
216:2x 2x 2x 3x 3x 3
306:2x 3x 3x 17
270:2x 3x 3x 3x 5
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 3x 3x 3x 3x 3x 17 = 16524
Therefore, the value for common factors is 16524.
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 = 4247328960/(2x16524)
LCM = 4247328960/33048
LCM = 128520
Thus, we can understand that the LCM of 238,216,306,270 is 128520.
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FAQs on LCM of 238, 216, 306, 270
1. What is the LCM of 238, 216, 306, 270?
Answer: LCM of 238, 216, 306, 270 is 128520.
2. How to calculate the LCM of 238, 216, 306, 270?
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, 216, 306, 270.
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}.