LCM of 105, 345, 175, 208
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 345, 175, 208 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 105, 345, 175, 208. So, keep reading to learn more.
Given numbers are 105,345,175,208
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,345,175,208 is 2511600.
Find LCM of 105,345,175,208 with Prime Factorization
| 3 | 105, 345, 175, 208 |
| 5 | 35, 115, 175, 208 |
| 7 | 7, 23, 35, 208 |
| 1, 23, 5, 208 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 7 x 1 x 23 x 5 x 208 = 2511600
Therefore, the lowest common multiple of 105,345,175,208 is 2511600.
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.
105 x 345 x 175 x 208 = 1318590000
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.
105 : 1, 3, 5, 7, 15, 21, 35, 105
345 : 1, 3, 5, 15, 23, 69, 115, 345
175 : 1, 5, 7, 25, 35, 175
208 : 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,345,175,208, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
345:3x 5x 23
175:5x 5x 7
208:2x 2x 2x 2x 13
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 5x 5x 7 = 525
Therefore, the value for common factors is 525.
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 = 1318590000/(1x525)
LCM = 1318590000/525
LCM = 2511600
Thus, we can understand that the LCM of 105,345,175,208 is 2511600.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 105, 345, 175, 208
1. What is the LCM of 105, 345, 175, 208?
Answer: LCM of 105, 345, 175, 208 is 2511600.
2. How to calculate the LCM of 105, 345, 175, 208?
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 105, 345, 175, 208.
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}.