LCM of 414, 505, 442, 221
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 414, 505, 442, 221 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 414, 505, 442, 221. So, keep reading to learn more.
Given numbers are 414,505,442,221
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 414,505,442,221 is 46204470.
Find LCM of 414,505,442,221 with Prime Factorization
| 2 | 414, 505, 442, 221 |
| 13 | 207, 505, 221, 221 |
| 17 | 207, 505, 17, 17 |
| 207, 505, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 13 x 17 x 207 x 505 x 1 x 1 = 46204470
Therefore, the lowest common multiple of 414,505,442,221 is 46204470.
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.
414 x 505 x 442 x 221 = 20422375740
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.
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
505 : 1, 5, 101, 505
442 : 1, 2, 13, 17, 26, 34, 221, 442
221 : 1, 13, 17, 221
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 414,505,442,221, is 1.
Now, the common factors can be found like this.
414:2x 3x 3x 23
505:5x 101
442:2x 13x 17
221:13x 17
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 13x 17 = 442
Therefore, the value for common factors is 442.
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 = 20422375740/(1x442)
LCM = 20422375740/442
LCM = 46204470
Thus, we can understand that the LCM of 414,505,442,221 is 46204470.
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FAQs on LCM of 414, 505, 442, 221
1. What is the LCM of 414, 505, 442, 221?
Answer: LCM of 414, 505, 442, 221 is 46204470.
2. How to calculate the LCM of 414, 505, 442, 221?
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 414, 505, 442, 221.
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}.