LCM of 330, 112, 408, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 330, 112, 408, 840 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 330, 112, 408, 840. So, keep reading to learn more.
Given numbers are 330,112,408,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 330,112,408,840 is 314160.
Find LCM of 330,112,408,840 with Prime Factorization
| 2 | 330, 112, 408, 840 |
| 2 | 165, 56, 204, 420 |
| 2 | 165, 28, 102, 210 |
| 3 | 165, 14, 51, 105 |
| 5 | 55, 14, 17, 35 |
| 7 | 11, 14, 17, 7 |
| 11, 2, 17, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 11 x 2 x 17 x 1 = 314160
Therefore, the lowest common multiple of 330,112,408,840 is 314160.
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.
330 x 112 x 408 x 840 = 12666931200
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.
330 : 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330
112 : 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 330,112,408,840, is 2.
Now, the common factors can be found like this.
330:2x 3x 5x 11
112:2x 2x 2x 2x 7
408:2x 2x 2x 3x 17
840:2x 2x 2x 3x 5x 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 2x 2x 2x 2x 2x 3x 3x 5x 7 = 20160
Therefore, the value for common factors is 20160.
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 = 12666931200/(2x20160)
LCM = 12666931200/40320
LCM = 314160
Thus, we can understand that the LCM of 330,112,408,840 is 314160.
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FAQs on LCM of 330, 112, 408, 840
1. What is the LCM of 330, 112, 408, 840?
Answer: LCM of 330, 112, 408, 840 is 314160.
2. How to calculate the LCM of 330, 112, 408, 840?
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 330, 112, 408, 840.
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}.