LCM of 320, 105, 300, 680
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 320, 105, 300, 680 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 320, 105, 300, 680. So, keep reading to learn more.
Given numbers are 320,105,300,680
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 320,105,300,680 is 571200.
Find LCM of 320,105,300,680 with Prime Factorization
| 2 | 320, 105, 300, 680 |
| 2 | 160, 105, 150, 340 |
| 2 | 80, 105, 75, 170 |
| 3 | 40, 105, 75, 85 |
| 5 | 40, 35, 25, 85 |
| 8, 7, 5, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 8 x 7 x 5 x 17 = 571200
Therefore, the lowest common multiple of 320,105,300,680 is 571200.
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.
320 x 105 x 300 x 680 = 6854400000
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.
320 : 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
105 : 1, 3, 5, 7, 15, 21, 35, 105
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
680 : 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
5 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 320,105,300,680, is 5.
Now, the common factors can be found like this.
320:2x 2x 2x 2x 2x 2x 5
105:3x 5x 7
300:2x 2x 3x 5x 5
680:2x 2x 2x 5x 17
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 3x 5x 5 = 2400
Therefore, the value for common factors is 2400.
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 = 6854400000/(5x2400)
LCM = 6854400000/12000
LCM = 571200
Thus, we can understand that the LCM of 320,105,300,680 is 571200.
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FAQs on LCM of 320, 105, 300, 680
1. What is the LCM of 320, 105, 300, 680?
Answer: LCM of 320, 105, 300, 680 is 571200.
2. How to calculate the LCM of 320, 105, 300, 680?
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 320, 105, 300, 680.
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}.