LCM of 112, 405, 456, 409
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 112, 405, 456, 409 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 112, 405, 456, 409. So, keep reading to learn more.
Given numbers are 112,405,456,409
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 112,405,456,409 is 352492560.
Find LCM of 112,405,456,409 with Prime Factorization
| 2 | 112, 405, 456, 409 |
| 2 | 56, 405, 228, 409 |
| 2 | 28, 405, 114, 409 |
| 3 | 14, 405, 57, 409 |
| 14, 135, 19, 409 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 14 x 135 x 19 x 409 = 352492560
Therefore, the lowest common multiple of 112,405,456,409 is 352492560.
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.
112 x 405 x 456 x 409 = 8459821440
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.
112 : 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
409 : 1, 409
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 112,405,456,409, is 1.
Now, the common factors can be found like this.
112:2x 2x 2x 2x 7
405:3x 3x 3x 3x 5
456:2x 2x 2x 3x 19
409:409
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 3 = 24
Therefore, the value for common factors is 24.
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 = 8459821440/(1x24)
LCM = 8459821440/24
LCM = 352492560
Thus, we can understand that the LCM of 112,405,456,409 is 352492560.
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FAQs on LCM of 112, 405, 456, 409
1. What is the LCM of 112, 405, 456, 409?
Answer: LCM of 112, 405, 456, 409 is 352492560.
2. How to calculate the LCM of 112, 405, 456, 409?
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 112, 405, 456, 409.
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}.