LCM of 414, 109, 132, 224
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 414, 109, 132, 224 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, 109, 132, 224. So, keep reading to learn more.
Given numbers are 414,109,132,224
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 414,109,132,224 is 55595232.
Find LCM of 414,109,132,224 with Prime Factorization
| 2 | 414, 109, 132, 224 |
| 2 | 207, 109, 66, 112 |
| 3 | 207, 109, 33, 56 |
| 69, 109, 11, 56 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 69 x 109 x 11 x 56 = 55595232
Therefore, the lowest common multiple of 414,109,132,224 is 55595232.
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 109 x 132 x 224 = 1334285568
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
109 : 1, 109
132 : 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 414,109,132,224, is 1.
Now, the common factors can be found like this.
414:2x 3x 3x 23
109:109
132:2x 2x 3x 11
224:2x 2x 2x 2x 2x 7
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 3 = 24
Therefore, the value for common factors is 24.
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 = 1334285568/(1x24)
LCM = 1334285568/24
LCM = 55595232
Thus, we can understand that the LCM of 414,109,132,224 is 55595232.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 414, 109, 132, 224
1. What is the LCM of 414, 109, 132, 224?
Answer: LCM of 414, 109, 132, 224 is 55595232.
2. How to calculate the LCM of 414, 109, 132, 224?
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, 109, 132, 224.
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}.