LCM of 105, 672, 408, 409, 457
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 672, 408, 409, 457 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, 672, 408, 409, 457. So, keep reading to learn more.
Given numbers are 105,672,408,409,457
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,672,408,409,457 is 10676470560.
Find LCM of 105,672,408,409,457 with Prime Factorization
| 2 | 105, 672, 408, 409, 457 |
| 2 | 105, 336, 204, 409, 457 |
| 2 | 105, 168, 102, 409, 457 |
| 3 | 105, 84, 51, 409, 457 |
| 7 | 35, 28, 17, 409, 457 |
| 5, 4, 17, 409, 457 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 7 x 5 x 4 x 17 x 409 x 457 = 10676470560
Therefore, the lowest common multiple of 105,672,408,409,457 is 10676470560.
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 672 x 408 x 409 x 457 = 5380941162240
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
672 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
409 : 1, 409
457 : 1, 457
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,672,408,409,457, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
672:2x 2x 2x 2x 2x 3x 7
408:2x 2x 2x 3x 17
409:409
457:457
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 3x 3x 7 = 504
Therefore, the value for common factors is 504.
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 = 5380941162240/(1x504)
LCM = 5380941162240/504
LCM = 10676470560
Thus, we can understand that the LCM of 105,672,408,409,457 is 10676470560.
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FAQs on LCM of 105, 672, 408, 409, 457
1. What is the LCM of 105, 672, 408, 409, 457?
Answer: LCM of 105, 672, 408, 409, 457 is 10676470560.
2. How to calculate the LCM of 105, 672, 408, 409, 457?
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, 672, 408, 409, 457.
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}.