LCM of 510, 360, 285, 178, 576
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 510, 360, 285, 178, 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 510, 360, 285, 178, 576. So, keep reading to learn more.
Given numbers are 510,360,285,178,576
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 510,360,285,178,576 is 82791360.
Find LCM of 510,360,285,178,576 with Prime Factorization
| 2 | 510, 360, 285, 178, 576 |
| 2 | 255, 180, 285, 89, 288 |
| 2 | 255, 90, 285, 89, 144 |
| 3 | 255, 45, 285, 89, 72 |
| 3 | 85, 15, 95, 89, 24 |
| 5 | 85, 5, 95, 89, 8 |
| 17, 1, 19, 89, 8 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 5 x 17 x 1 x 19 x 89 x 8 = 82791360
Therefore, the lowest common multiple of 510,360,285,178,576 is 82791360.
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.
510 x 360 x 285 x 178 x 576 = 5364880128000
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.
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
360 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
285 : 1, 3, 5, 15, 19, 57, 95, 285
178 : 1, 2, 89, 178
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 510,360,285,178,576, is 1.
Now, the common factors can be found like this.
510:2x 3x 5x 17
360:2x 2x 2x 3x 3x 5
285:3x 5x 19
178:2x 89
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 2x 2x 3x 3x 3x 3x 5x 5 = 64800
Therefore, the value for common factors is 64800.
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 = 5364880128000/(1x64800)
LCM = 5364880128000/64800
LCM = 82791360
Thus, we can understand that the LCM of 510,360,285,178,576 is 82791360.
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FAQs on LCM of 510, 360, 285, 178, 576
1. What is the LCM of 510, 360, 285, 178, 576?
Answer: LCM of 510, 360, 285, 178, 576 is 82791360.
2. How to calculate the LCM of 510, 360, 285, 178, 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 510, 360, 285, 178, 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}.