LCM of 165, 185, 212, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 165, 185, 212, 414 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 165, 185, 212, 414. So, keep reading to learn more.
Given numbers are 165,185,212,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 165,185,212,414 is 89303940.
Find LCM of 165,185,212,414 with Prime Factorization
| 2 | 165, 185, 212, 414 |
| 3 | 165, 185, 106, 207 |
| 5 | 55, 185, 106, 69 |
| 11, 37, 106, 69 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 11 x 37 x 106 x 69 = 89303940
Therefore, the lowest common multiple of 165,185,212,414 is 89303940.
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.
165 x 185 x 212 x 414 = 2679118200
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.
165 : 1, 3, 5, 11, 15, 33, 55, 165
185 : 1, 5, 37, 185
212 : 1, 2, 4, 53, 106, 212
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 165,185,212,414, is 1.
Now, the common factors can be found like this.
165:3x 5x 11
185:5x 37
212:2x 2x 53
414:2x 3x 3x 23
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 5 = 30
Therefore, the value for common factors is 30.
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 = 2679118200/(1x30)
LCM = 2679118200/30
LCM = 89303940
Thus, we can understand that the LCM of 165,185,212,414 is 89303940.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 165, 185, 212, 414
1. What is the LCM of 165, 185, 212, 414?
Answer: LCM of 165, 185, 212, 414 is 89303940.
2. How to calculate the LCM of 165, 185, 212, 414?
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 165, 185, 212, 414.
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}.