LCM of 578, 406, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 578, 406, 105 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 578, 406, 105. So, keep reading to learn more.
Given numbers are 578,406,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 578,406,105 is 1760010.
Find LCM of 578,406,105 with Prime Factorization
| 2 | 578, 406, 105 |
| 7 | 289, 203, 105 |
| 289, 29, 15 |
Multiply the prime numbers at the bottom and the left side.
2 x 7 x 289 x 29 x 15 = 1760010
Therefore, the lowest common multiple of 578,406,105 is 1760010.
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.
578 x 406 x 105 = 24640140
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.
578 : 1, 2, 17, 34, 289, 578
406 : 1, 2, 7, 14, 29, 58, 203, 406
105 : 1, 3, 5, 7, 15, 21, 35, 105
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 578,406,105, is 1.
Now, the common factors can be found like this.
578:2x 17x 17
406:2x 7x 29
105:3x 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 7 = 14
Therefore, the value for common factors is 14.
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 = 24640140/(1x14)
LCM = 24640140/14
LCM = 1760010
Thus, we can understand that the LCM of 578,406,105 is 1760010.
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FAQs on LCM of 578, 406, 105
1. What is the LCM of 578, 406, 105?
Answer: LCM of 578, 406, 105 is 1760010.
2. How to calculate the LCM of 578, 406, 105?
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 578, 406, 105.
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}.