LCM of 105, 401, 420, 617
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 401, 420, 617 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 105, 401, 420, 617. So, keep reading to learn more.
Given numbers are 105,401,420,617
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,401,420,617 is 103915140.
Find LCM of 105,401,420,617 with Prime Factorization
| 3 | 105, 401, 420, 617 |
| 5 | 35, 401, 140, 617 |
| 7 | 7, 401, 28, 617 |
| 1, 401, 4, 617 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 7 x 1 x 401 x 4 x 617 = 103915140
Therefore, the lowest common multiple of 105,401,420,617 is 103915140.
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.
105 x 401 x 420 x 617 = 10911089700
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.
105 : 1, 3, 5, 7, 15, 21, 35, 105
401 : 1, 401
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
617 : 1, 617
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,401,420,617, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
401:401
420:2x 2x 3x 5x 7
617:617
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 5x 7 = 105
Therefore, the value for common factors is 105.
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 = 10911089700/(1x105)
LCM = 10911089700/105
LCM = 103915140
Thus, we can understand that the LCM of 105,401,420,617 is 103915140.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 105, 401, 420, 617
1. What is the LCM of 105, 401, 420, 617?
Answer: LCM of 105, 401, 420, 617 is 103915140.
2. How to calculate the LCM of 105, 401, 420, 617?
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 105, 401, 420, 617.
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}.