LCM of 600, 756, 512, 315, 648
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 600, 756, 512, 315, 648 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 600, 756, 512, 315, 648. So, keep reading to learn more.
Given numbers are 600,756,512,315,648
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 600,756,512,315,648 is 7257600.
Find LCM of 600,756,512,315,648 with Prime Factorization
| 2 | 600, 756, 512, 315, 648 |
| 2 | 300, 378, 256, 315, 324 |
| 2 | 150, 189, 128, 315, 162 |
| 3 | 75, 189, 64, 315, 81 |
| 3 | 25, 63, 64, 105, 27 |
| 3 | 25, 21, 64, 35, 9 |
| 5 | 25, 7, 64, 35, 3 |
| 7 | 5, 7, 64, 7, 3 |
| 5, 1, 64, 1, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 5 x 1 x 64 x 1 x 3 = 7257600
Therefore, the lowest common multiple of 600,756,512,315,648 is 7257600.
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.
600 x 756 x 512 x 315 x 648 = 47405481984000
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.
600 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
756 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
648 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 600,756,512,315,648, is 1.
Now, the common factors can be found like this.
600:2x 2x 2x 3x 5x 5
756:2x 2x 3x 3x 3x 7
512:2x 2x 2x 2x 2x 2x 2x 2x 2
315:3x 3x 5x 7
648:2x 2x 2x 3x 3x 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 2x 2x 2x 3x 3x 3x 3x 3x 3x 5x 7 = 6531840
Therefore, the value for common factors is 6531840.
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 = 47405481984000/(1x6531840)
LCM = 47405481984000/6531840
LCM = 7257600
Thus, we can understand that the LCM of 600,756,512,315,648 is 7257600.
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FAQs on LCM of 600, 756, 512, 315, 648
1. What is the LCM of 600, 756, 512, 315, 648?
Answer: LCM of 600, 756, 512, 315, 648 is 7257600.
2. How to calculate the LCM of 600, 756, 512, 315, 648?
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 600, 756, 512, 315, 648.
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}.