LCM of 3, 105, 102, 168
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 3, 105, 102, 168 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 3, 105, 102, 168. So, keep reading to learn more.
Given numbers are 3,105,102,168
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 3,105,102,168 is 14280.
Find LCM of 3,105,102,168 with Prime Factorization
| 2 | 3, 105, 102, 168 |
| 3 | 3, 105, 51, 84 |
| 7 | 1, 35, 17, 28 |
| 1, 5, 17, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 7 x 1 x 5 x 17 x 4 = 14280
Therefore, the lowest common multiple of 3,105,102,168 is 14280.
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.
3 x 105 x 102 x 168 = 5397840
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.
3 : 1, 3
105 : 1, 3, 5, 7, 15, 21, 35, 105
102 : 1, 2, 3, 6, 17, 34, 51, 102
168 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 3,105,102,168, is 3.
Now, the common factors can be found like this.
3:3
105:3x 5x 7
102:2x 3x 17
168:2x 2x 2x 3x 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 3x 3x 7 = 126
Therefore, the value for common factors is 126.
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 = 5397840/(3x126)
LCM = 5397840/378
LCM = 14280
Thus, we can understand that the LCM of 3,105,102,168 is 14280.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 3, 105, 102, 168
1. What is the LCM of 3, 105, 102, 168?
Answer: LCM of 3, 105, 102, 168 is 14280.
2. How to calculate the LCM of 3, 105, 102, 168?
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 3, 105, 102, 168.
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}.