LCM of 345, 168, 405, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 345, 168, 405, 312 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 345, 168, 405, 312. So, keep reading to learn more.
Given numbers are 345,168,405,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 345,168,405,312 is 6781320.
Find LCM of 345,168,405,312 with Prime Factorization
| 2 | 345, 168, 405, 312 |
| 2 | 345, 84, 405, 156 |
| 2 | 345, 42, 405, 78 |
| 3 | 345, 21, 405, 39 |
| 5 | 115, 7, 135, 13 |
| 23, 7, 27, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 23 x 7 x 27 x 13 = 6781320
Therefore, the lowest common multiple of 345,168,405,312 is 6781320.
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.
345 x 168 x 405 x 312 = 7323825600
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.
345 : 1, 3, 5, 15, 23, 69, 115, 345
168 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 345,168,405,312, is 3.
Now, the common factors can be found like this.
345:3x 5x 23
168:2x 2x 2x 3x 7
405:3x 3x 3x 3x 5
312:2x 2x 2x 3x 13
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 2x 3x 3x 5 = 360
Therefore, the value for common factors is 360.
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 = 7323825600/(3x360)
LCM = 7323825600/1080
LCM = 6781320
Thus, we can understand that the LCM of 345,168,405,312 is 6781320.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 345, 168, 405, 312
1. What is the LCM of 345, 168, 405, 312?
Answer: LCM of 345, 168, 405, 312 is 6781320.
2. How to calculate the LCM of 345, 168, 405, 312?
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 345, 168, 405, 312.
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}.