LCM of 209, 105, 140, 165
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 209, 105, 140, 165 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, 105, 140, 165. So, keep reading to learn more.
Given numbers are 209,105,140,165
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 209,105,140,165 is 87780.
Find LCM of 209,105,140,165 with Prime Factorization
| 3 | 209, 105, 140, 165 |
| 5 | 209, 35, 140, 55 |
| 7 | 209, 7, 28, 11 |
| 11 | 209, 1, 4, 11 |
| 19, 1, 4, 1 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 7 x 11 x 19 x 1 x 4 x 1 = 87780
Therefore, the lowest common multiple of 209,105,140,165 is 87780.
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 105 x 140 x 165 = 506929500
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
105 : 1, 3, 5, 7, 15, 21, 35, 105
140 : 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
165 : 1, 3, 5, 11, 15, 33, 55, 165
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 209,105,140,165, is 1.
Now, the common factors can be found like this.
209:11x 19
105:3x 5x 7
140:2x 2x 5x 7
165:3x 5x 11
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 5x 5x 7x 11 = 5775
Therefore, the value for common factors is 5775.
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 = 506929500/(1x5775)
LCM = 506929500/5775
LCM = 87780
Thus, we can understand that the LCM of 209,105,140,165 is 87780.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 209, 105, 140, 165
1. What is the LCM of 209, 105, 140, 165?
Answer: LCM of 209, 105, 140, 165 is 87780.
2. How to calculate the LCM of 209, 105, 140, 165?
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, 105, 140, 165.
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}.