LCM of 576, 225, 408, 624
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 576, 225, 408, 624 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 576, 225, 408, 624. So, keep reading to learn more.
Given numbers are 576,225,408,624
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 576,225,408,624 is 3182400.
Find LCM of 576,225,408,624 with Prime Factorization
| 2 | 576, 225, 408, 624 |
| 2 | 288, 225, 204, 312 |
| 2 | 144, 225, 102, 156 |
| 2 | 72, 225, 51, 78 |
| 3 | 36, 225, 51, 39 |
| 3 | 12, 75, 17, 13 |
| 4, 25, 17, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 4 x 25 x 17 x 13 = 3182400
Therefore, the lowest common multiple of 576,225,408,624 is 3182400.
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.
576 x 225 x 408 x 624 = 32995123200
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.
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
225 : 1, 3, 5, 9, 15, 25, 45, 75, 225
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
624 : 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 576,225,408,624, is 3.
Now, the common factors can be found like this.
576:2x 2x 2x 2x 2x 2x 3x 3
225:3x 3x 5x 5
408:2x 2x 2x 3x 17
624:2x 2x 2x 2x 3x 13
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 3x 3x 3 = 3456
Therefore, the value for common factors is 3456.
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 = 32995123200/(3x3456)
LCM = 32995123200/10368
LCM = 3182400
Thus, we can understand that the LCM of 576,225,408,624 is 3182400.
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FAQs on LCM of 576, 225, 408, 624
1. What is the LCM of 576, 225, 408, 624?
Answer: LCM of 576, 225, 408, 624 is 3182400.
2. How to calculate the LCM of 576, 225, 408, 624?
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 576, 225, 408, 624.
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}.