LCM of 768, 214, 348, 407
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 768, 214, 348, 407 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 768, 214, 348, 407. So, keep reading to learn more.
Given numbers are 768,214,348,407
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 768,214,348,407 is 969923328.
Find LCM of 768,214,348,407 with Prime Factorization
| 2 | 768, 214, 348, 407 |
| 2 | 384, 107, 174, 407 |
| 3 | 192, 107, 87, 407 |
| 64, 107, 29, 407 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 64 x 107 x 29 x 407 = 969923328
Therefore, the lowest common multiple of 768,214,348,407 is 969923328.
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.
768 x 214 x 348 x 407 = 23278159872
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.
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
214 : 1, 2, 107, 214
348 : 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
407 : 1, 11, 37, 407
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 768,214,348,407, is 1.
Now, the common factors can be found like this.
768:2x 2x 2x 2x 2x 2x 2x 2x 3
214:2x 107
348:2x 2x 3x 29
407:11x 37
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 3 = 24
Therefore, the value for common factors is 24.
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 = 23278159872/(1x24)
LCM = 23278159872/24
LCM = 969923328
Thus, we can understand that the LCM of 768,214,348,407 is 969923328.
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FAQs on LCM of 768, 214, 348, 407
1. What is the LCM of 768, 214, 348, 407?
Answer: LCM of 768, 214, 348, 407 is 969923328.
2. How to calculate the LCM of 768, 214, 348, 407?
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 768, 214, 348, 407.
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}.