LCM of 512, 224, 200, 414, 306
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 512, 224, 200, 414, 306 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 512, 224, 200, 414, 306. So, keep reading to learn more.
Given numbers are 512,224,200,414,306
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 512,224,200,414,306 is 315302400.
Find LCM of 512,224,200,414,306 with Prime Factorization
| 2 | 512, 224, 200, 414, 306 |
| 2 | 256, 112, 100, 207, 153 |
| 2 | 128, 56, 50, 207, 153 |
| 2 | 64, 28, 25, 207, 153 |
| 2 | 32, 14, 25, 207, 153 |
| 3 | 16, 7, 25, 207, 153 |
| 3 | 16, 7, 25, 69, 51 |
| 16, 7, 25, 23, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 3 x 3 x 16 x 7 x 25 x 23 x 17 = 315302400
Therefore, the lowest common multiple of 512,224,200,414,306 is 315302400.
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.
512 x 224 x 200 x 414 x 306 = 2905826918400
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.
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 512,224,200,414,306, is 2.
Now, the common factors can be found like this.
512:2x 2x 2x 2x 2x 2x 2x 2x 2
224:2x 2x 2x 2x 2x 7
200:2x 2x 2x 5x 5
414:2x 3x 3x 23
306:2x 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 2x 2x 2x 2x 2x 2x 3x 3 = 4608
Therefore, the value for common factors is 4608.
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 = 2905826918400/(2x4608)
LCM = 2905826918400/9216
LCM = 315302400
Thus, we can understand that the LCM of 512,224,200,414,306 is 315302400.
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FAQs on LCM of 512, 224, 200, 414, 306
1. What is the LCM of 512, 224, 200, 414, 306?
Answer: LCM of 512, 224, 200, 414, 306 is 315302400.
2. How to calculate the LCM of 512, 224, 200, 414, 306?
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 512, 224, 200, 414, 306.
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}.