Find the LCM of 460, 462, 216, 240, 309 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 460, 462, 216, 240, 309. So, keep reading to learn more.
Given numbers are 460,462,216,240,309
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 460,462,216,240,309 is 394012080.
Find LCM of 460,462,216,240,309 with Prime Factorization
2 | 460, 462, 216, 240, 309 |
2 | 230, 231, 108, 120, 309 |
2 | 115, 231, 54, 60, 309 |
3 | 115, 231, 27, 30, 309 |
5 | 115, 77, 9, 10, 103 |
23, 77, 9, 2, 103 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 23 x 77 x 9 x 2 x 103 = 394012080
Therefore, the lowest common multiple of 460,462,216,240,309 is 394012080.
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.
460 x 462 x 216 x 240 x 309 = 3404264371200
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.
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
462 : 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
309 : 1, 3, 103, 309
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 460,462,216,240,309, is 1.
Now, the common factors can be found like this.
460:2x 2x 5x 23
462:2x 3x 7x 11
216:2x 2x 2x 3x 3x 3
240:2x 2x 2x 2x 3x 5
309:3x 103
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 2x 2x 2x 3x 3x 3x 5 = 8640
Therefore, the value for common factors is 8640.
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 = 3404264371200/(1x8640)
LCM = 3404264371200/8640
LCM = 394012080
Thus, we can understand that the LCM of 460,462,216,240,309 is 394012080.
Here are some samples of LCM of two or more Numbers calculations.
1. What is the LCM of 460, 462, 216, 240, 309?
Answer: LCM of 460, 462, 216, 240, 309 is 394012080.
2. How to calculate the LCM of 460, 462, 216, 240, 309?
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 460, 462, 216, 240, 309.
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}.