LCM of 564, 450, 842, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 564, 450, 842, 900 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 564, 450, 842, 900. So, keep reading to learn more.
Given numbers are 564,450,842,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 564,450,842,900 is 17808300.
Find LCM of 564,450,842,900 with Prime Factorization
| 2 | 564, 450, 842, 900 |
| 2 | 282, 225, 421, 450 |
| 3 | 141, 225, 421, 225 |
| 3 | 47, 75, 421, 75 |
| 5 | 47, 25, 421, 25 |
| 5 | 47, 5, 421, 5 |
| 47, 1, 421, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 5 x 47 x 1 x 421 x 1 = 17808300
Therefore, the lowest common multiple of 564,450,842,900 is 17808300.
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.
564 x 450 x 842 x 900 = 192329640000
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.
564 : 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
450 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
842 : 1, 2, 421, 842
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 564,450,842,900, is 2.
Now, the common factors can be found like this.
564:2x 2x 3x 47
450:2x 3x 3x 5x 5
842:2x 421
900:2x 2x 3x 3x 5x 5
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 3x 5x 5 = 5400
Therefore, the value for common factors is 5400.
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 = 192329640000/(2x5400)
LCM = 192329640000/10800
LCM = 17808300
Thus, we can understand that the LCM of 564,450,842,900 is 17808300.
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FAQs on LCM of 564, 450, 842, 900
1. What is the LCM of 564, 450, 842, 900?
Answer: LCM of 564, 450, 842, 900 is 17808300.
2. How to calculate the LCM of 564, 450, 842, 900?
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 564, 450, 842, 900.
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}.