LCM of 230, 210, 317, 450, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 230, 210, 317, 450, 105 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 230, 210, 317, 450, 105. So, keep reading to learn more.
Given numbers are 230,210,317,450,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 230,210,317,450,105 is 22966650.
Find LCM of 230,210,317,450,105 with Prime Factorization
| 2 | 230, 210, 317, 450, 105 |
| 3 | 115, 105, 317, 225, 105 |
| 5 | 115, 35, 317, 75, 35 |
| 7 | 23, 7, 317, 15, 7 |
| 23, 1, 317, 15, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 23 x 1 x 317 x 15 x 1 = 22966650
Therefore, the lowest common multiple of 230,210,317,450,105 is 22966650.
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.
230 x 210 x 317 x 450 x 105 = 723449475000
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.
230 : 1, 2, 5, 10, 23, 46, 115, 230
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
317 : 1, 317
450 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
105 : 1, 3, 5, 7, 15, 21, 35, 105
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 230,210,317,450,105, is 1.
Now, the common factors can be found like this.
230:2x 5x 23
210:2x 3x 5x 7
317:317
450:2x 3x 3x 5x 5
105:3x 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 3x 3x 5x 5x 5x 7 = 31500
Therefore, the value for common factors is 31500.
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 = 723449475000/(1x31500)
LCM = 723449475000/31500
LCM = 22966650
Thus, we can understand that the LCM of 230,210,317,450,105 is 22966650.
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FAQs on LCM of 230, 210, 317, 450, 105
1. What is the LCM of 230, 210, 317, 450, 105?
Answer: LCM of 230, 210, 317, 450, 105 is 22966650.
2. How to calculate the LCM of 230, 210, 317, 450, 105?
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 230, 210, 317, 450, 105.
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}.