LCM of 417, 111, 288, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 417, 111, 288, 420 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 417, 111, 288, 420. So, keep reading to learn more.
Given numbers are 417,111,288,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 417,111,288,420 is 51841440.
Find LCM of 417,111,288,420 with Prime Factorization
| 2 | 417, 111, 288, 420 |
| 2 | 417, 111, 144, 210 |
| 3 | 417, 111, 72, 105 |
| 139, 37, 24, 35 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 139 x 37 x 24 x 35 = 51841440
Therefore, the lowest common multiple of 417,111,288,420 is 51841440.
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.
417 x 111 x 288 x 420 = 5598875520
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.
417 : 1, 3, 139, 417
111 : 1, 3, 37, 111
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
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
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 417,111,288,420, is 3.
Now, the common factors can be found like this.
417:3x 139
111:3x 37
288:2x 2x 2x 2x 2x 3x 3
420:2x 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 3x 3 = 36
Therefore, the value for common factors is 36.
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 = 5598875520/(3x36)
LCM = 5598875520/108
LCM = 51841440
Thus, we can understand that the LCM of 417,111,288,420 is 51841440.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 417, 111, 288, 420
1. What is the LCM of 417, 111, 288, 420?
Answer: LCM of 417, 111, 288, 420 is 51841440.
2. How to calculate the LCM of 417, 111, 288, 420?
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 417, 111, 288, 420.
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}.