LCM of 680, 768, 210
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 680, 768, 210 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 680, 768, 210. So, keep reading to learn more.
Given numbers are 680,768,210
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 680,768,210 is 456960.
Find LCM of 680,768,210 with Prime Factorization
| 2 | 680, 768, 210 |
| 2 | 340, 384, 105 |
| 2 | 170, 192, 105 |
| 3 | 85, 96, 105 |
| 5 | 85, 32, 35 |
| 17, 32, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 17 x 32 x 7 = 456960
Therefore, the lowest common multiple of 680,768,210 is 456960.
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.
680 x 768 x 210 = 109670400
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.
680 : 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 680,768,210, is 2.
Now, the common factors can be found like this.
680:2x 2x 2x 5x 17
768:2x 2x 2x 2x 2x 2x 2x 2x 3
210:2x 3x 5x 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 3x 5 = 120
Therefore, the value for common factors is 120.
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 = 109670400/(2x120)
LCM = 109670400/240
LCM = 456960
Thus, we can understand that the LCM of 680,768,210 is 456960.
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FAQs on LCM of 680, 768, 210
1. What is the LCM of 680, 768, 210?
Answer: LCM of 680, 768, 210 is 456960.
2. How to calculate the LCM of 680, 768, 210?
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 680, 768, 210.
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}.