LCM of 820, 768, 464, 378, 189
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 820, 768, 464, 378, 189 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 820, 768, 464, 378, 189. So, keep reading to learn more.
Given numbers are 820,768,464,378,189
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 820,768,464,378,189 is 287642880.
Find LCM of 820,768,464,378,189 with Prime Factorization
| 2 | 820, 768, 464, 378, 189 |
| 2 | 410, 384, 232, 189, 189 |
| 2 | 205, 192, 116, 189, 189 |
| 2 | 205, 96, 58, 189, 189 |
| 3 | 205, 48, 29, 189, 189 |
| 3 | 205, 16, 29, 63, 63 |
| 3 | 205, 16, 29, 21, 21 |
| 7 | 205, 16, 29, 7, 7 |
| 205, 16, 29, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 205 x 16 x 29 x 1 x 1 = 287642880
Therefore, the lowest common multiple of 820,768,464,378,189 is 287642880.
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.
820 x 768 x 464 x 378 x 189 = 20875969658880
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.
820 : 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
464 : 1, 2, 4, 8, 16, 29, 58, 116, 232, 464
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
189 : 1, 3, 7, 9, 21, 27, 63, 189
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 820,768,464,378,189, is 1.
Now, the common factors can be found like this.
820:2x 2x 5x 41
768:2x 2x 2x 2x 2x 2x 2x 2x 3
464:2x 2x 2x 2x 29
378:2x 3x 3x 3x 7
189:3x 3x 3x 7
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 3x 3x 3x 3x 7 = 72576
Therefore, the value for common factors is 72576.
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 = 20875969658880/(1x72576)
LCM = 20875969658880/72576
LCM = 287642880
Thus, we can understand that the LCM of 820,768,464,378,189 is 287642880.
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FAQs on LCM of 820, 768, 464, 378, 189
1. What is the LCM of 820, 768, 464, 378, 189?
Answer: LCM of 820, 768, 464, 378, 189 is 287642880.
2. How to calculate the LCM of 820, 768, 464, 378, 189?
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 820, 768, 464, 378, 189.
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}.