LCM of 224, 512, 192, 728
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 224, 512, 192, 728 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 224, 512, 192, 728. So, keep reading to learn more.
Given numbers are 224,512,192,728
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 224,512,192,728 is 139776.
Find LCM of 224,512,192,728 with Prime Factorization
| 2 | 224, 512, 192, 728 |
| 2 | 112, 256, 96, 364 |
| 2 | 56, 128, 48, 182 |
| 2 | 28, 64, 24, 91 |
| 2 | 14, 32, 12, 91 |
| 2 | 7, 16, 6, 91 |
| 7 | 7, 8, 3, 91 |
| 1, 8, 3, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 2 x 7 x 1 x 8 x 3 x 13 = 139776
Therefore, the lowest common multiple of 224,512,192,728 is 139776.
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.
224 x 512 x 192 x 728 = 16030629888
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.
224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
8 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 224,512,192,728, is 8.
Now, the common factors can be found like this.
224:2x 2x 2x 2x 2x 7
512:2x 2x 2x 2x 2x 2x 2x 2x 2
192:2x 2x 2x 2x 2x 2x 3
728:2x 2x 2x 7x 13
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 2x 2x 7 = 14336
Therefore, the value for common factors is 14336.
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 = 16030629888/(8x14336)
LCM = 16030629888/114688
LCM = 139776
Thus, we can understand that the LCM of 224,512,192,728 is 139776.
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FAQs on LCM of 224, 512, 192, 728
1. What is the LCM of 224, 512, 192, 728?
Answer: LCM of 224, 512, 192, 728 is 139776.
2. How to calculate the LCM of 224, 512, 192, 728?
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 224, 512, 192, 728.
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}.