LCM of 310, 238, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 310, 238, 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 310, 238, 105. So, keep reading to learn more.
Given numbers are 310,238,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 310,238,105 is 110670.
Find LCM of 310,238,105 with Prime Factorization
| 2 | 310, 238, 105 |
| 5 | 155, 119, 105 |
| 7 | 31, 119, 21 |
| 31, 17, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 5 x 7 x 31 x 17 x 3 = 110670
Therefore, the lowest common multiple of 310,238,105 is 110670.
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.
310 x 238 x 105 = 7746900
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.
310 : 1, 2, 5, 10, 31, 62, 155, 310
238 : 1, 2, 7, 14, 17, 34, 119, 238
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 310,238,105, is 1.
Now, the common factors can be found like this.
310:2x 5x 31
238:2x 7x 17
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 5x 7 = 70
Therefore, the value for common factors is 70.
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 = 7746900/(1x70)
LCM = 7746900/70
LCM = 110670
Thus, we can understand that the LCM of 310,238,105 is 110670.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 310, 238, 105
1. What is the LCM of 310, 238, 105?
Answer: LCM of 310, 238, 105 is 110670.
2. How to calculate the LCM of 310, 238, 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 310, 238, 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}.