LCM of 209, 200, 105, 524
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 209, 200, 105, 524 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 209, 200, 105, 524. So, keep reading to learn more.
Given numbers are 209,200,105,524
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 209,200,105,524 is 114991800.
Find LCM of 209,200,105,524 with Prime Factorization
| 2 | 209, 200, 105, 524 |
| 2 | 209, 100, 105, 262 |
| 5 | 209, 50, 105, 131 |
| 209, 10, 21, 131 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 5 x 209 x 10 x 21 x 131 = 114991800
Therefore, the lowest common multiple of 209,200,105,524 is 114991800.
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.
209 x 200 x 105 x 524 = 2299836000
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.
209 : 1, 11, 19, 209
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
105 : 1, 3, 5, 7, 15, 21, 35, 105
524 : 1, 2, 4, 131, 262, 524
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 209,200,105,524, is 1.
Now, the common factors can be found like this.
209:11x 19
200:2x 2x 2x 5x 5
105:3x 5x 7
524:2x 2x 131
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 5 = 20
Therefore, the value for common factors is 20.
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 = 2299836000/(1x20)
LCM = 2299836000/20
LCM = 114991800
Thus, we can understand that the LCM of 209,200,105,524 is 114991800.
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FAQs on LCM of 209, 200, 105, 524
1. What is the LCM of 209, 200, 105, 524?
Answer: LCM of 209, 200, 105, 524 is 114991800.
2. How to calculate the LCM of 209, 200, 105, 524?
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 209, 200, 105, 524.
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}.