LCM of 705, 114, 123, 228, 768
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 705, 114, 123, 228, 768 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 705, 114, 123, 228, 768. So, keep reading to learn more.
Given numbers are 705,114,123,228,768
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 705,114,123,228,768 is 140593920.
Find LCM of 705,114,123,228,768 with Prime Factorization
| 2 | 705, 114, 123, 228, 768 |
| 2 | 705, 57, 123, 114, 384 |
| 3 | 705, 57, 123, 57, 192 |
| 19 | 235, 19, 41, 19, 64 |
| 235, 1, 41, 1, 64 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 19 x 235 x 1 x 41 x 1 x 64 = 140593920
Therefore, the lowest common multiple of 705,114,123,228,768 is 140593920.
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.
705 x 114 x 123 x 228 x 768 = 1730992343040
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.
705 : 1, 3, 5, 15, 47, 141, 235, 705
114 : 1, 2, 3, 6, 19, 38, 57, 114
123 : 1, 3, 41, 123
228 : 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 705,114,123,228,768, is 3.
Now, the common factors can be found like this.
705:3x 5x 47
114:2x 3x 19
123:3x 41
228:2x 2x 3x 19
768:2x 2x 2x 2x 2x 2x 2x 2x 3
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 3x 3x 19 = 4104
Therefore, the value for common factors is 4104.
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 = 1730992343040/(3x4104)
LCM = 1730992343040/12312
LCM = 140593920
Thus, we can understand that the LCM of 705,114,123,228,768 is 140593920.
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FAQs on LCM of 705, 114, 123, 228, 768
1. What is the LCM of 705, 114, 123, 228, 768?
Answer: LCM of 705, 114, 123, 228, 768 is 140593920.
2. How to calculate the LCM of 705, 114, 123, 228, 768?
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 705, 114, 123, 228, 768.
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}.