LCM of 465, 115, 300, 870, 986
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 465, 115, 300, 870, 986 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 465, 115, 300, 870, 986. So, keep reading to learn more.
Given numbers are 465,115,300,870,986
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 465,115,300,870,986 is 105452700.
Find LCM of 465,115,300,870,986 with Prime Factorization
| 2 | 465, 115, 300, 870, 986 |
| 3 | 465, 115, 150, 435, 493 |
| 5 | 155, 115, 50, 145, 493 |
| 29 | 31, 23, 10, 29, 493 |
| 31, 23, 10, 1, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 29 x 31 x 23 x 10 x 1 x 17 = 105452700
Therefore, the lowest common multiple of 465,115,300,870,986 is 105452700.
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.
465 x 115 x 300 x 870 x 986 = 13761577350000
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.
465 : 1, 3, 5, 15, 31, 93, 155, 465
115 : 1, 5, 23, 115
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
870 : 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
986 : 1, 2, 17, 29, 34, 58, 493, 986
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 465,115,300,870,986, is 1.
Now, the common factors can be found like this.
465:3x 5x 31
115:5x 23
300:2x 2x 3x 5x 5
870:2x 3x 5x 29
986:2x 17x 29
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 29 = 130500
Therefore, the value for common factors is 130500.
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 = 13761577350000/(1x130500)
LCM = 13761577350000/130500
LCM = 105452700
Thus, we can understand that the LCM of 465,115,300,870,986 is 105452700.
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FAQs on LCM of 465, 115, 300, 870, 986
1. What is the LCM of 465, 115, 300, 870, 986?
Answer: LCM of 465, 115, 300, 870, 986 is 105452700.
2. How to calculate the LCM of 465, 115, 300, 870, 986?
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 465, 115, 300, 870, 986.
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}.