LCM of 492, 465, 678, 576
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 492, 465, 678, 576 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 492, 465, 678, 576. So, keep reading to learn more.
Given numbers are 492,465,678,576
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 492,465,678,576 is 413634240.
Find LCM of 492,465,678,576 with Prime Factorization
| 2 | 492, 465, 678, 576 |
| 2 | 246, 465, 339, 288 |
| 3 | 123, 465, 339, 144 |
| 41, 155, 113, 48 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 41 x 155 x 113 x 48 = 413634240
Therefore, the lowest common multiple of 492,465,678,576 is 413634240.
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.
492 x 465 x 678 x 576 = 89344995840
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.
492 : 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492
465 : 1, 3, 5, 15, 31, 93, 155, 465
678 : 1, 2, 3, 6, 113, 226, 339, 678
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 492,465,678,576, is 3.
Now, the common factors can be found like this.
492:2x 2x 3x 41
465:3x 5x 31
678:2x 3x 113
576:2x 2x 2x 2x 2x 2x 3x 3
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 3 = 72
Therefore, the value for common factors is 72.
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 = 89344995840/(3x72)
LCM = 89344995840/216
LCM = 413634240
Thus, we can understand that the LCM of 492,465,678,576 is 413634240.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 492, 465, 678, 576
1. What is the LCM of 492, 465, 678, 576?
Answer: LCM of 492, 465, 678, 576 is 413634240.
2. How to calculate the LCM of 492, 465, 678, 576?
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 492, 465, 678, 576.
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}.