LCM of 384, 660, 414, 174, 506
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 384, 660, 414, 174, 506 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 384, 660, 414, 174, 506. So, keep reading to learn more.
Given numbers are 384,660,414,174,506
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 384,660,414,174,506 is 42261120.
Find LCM of 384,660,414,174,506 with Prime Factorization
| 2 | 384, 660, 414, 174, 506 |
| 2 | 192, 330, 207, 87, 253 |
| 3 | 96, 165, 207, 87, 253 |
| 11 | 32, 55, 69, 29, 253 |
| 23 | 32, 5, 69, 29, 23 |
| 32, 5, 3, 29, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 11 x 23 x 32 x 5 x 3 x 29 x 1 = 42261120
Therefore, the lowest common multiple of 384,660,414,174,506 is 42261120.
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.
384 x 660 x 414 x 174 x 506 = 9237942743040
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.
384 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
660 : 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
174 : 1, 2, 3, 6, 29, 58, 87, 174
506 : 1, 2, 11, 22, 23, 46, 253, 506
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 384,660,414,174,506, is 2.
Now, the common factors can be found like this.
384:2x 2x 2x 2x 2x 2x 2x 3
660:2x 2x 3x 5x 11
414:2x 3x 3x 23
174:2x 3x 29
506:2x 11x 23
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 3x 3x 3x 11x 23 = 109296
Therefore, the value for common factors is 109296.
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 = 9237942743040/(2x109296)
LCM = 9237942743040/218592
LCM = 42261120
Thus, we can understand that the LCM of 384,660,414,174,506 is 42261120.
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FAQs on LCM of 384, 660, 414, 174, 506
1. What is the LCM of 384, 660, 414, 174, 506?
Answer: LCM of 384, 660, 414, 174, 506 is 42261120.
2. How to calculate the LCM of 384, 660, 414, 174, 506?
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 384, 660, 414, 174, 506.
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}.