LCM of 148, 321, 460, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 148, 321, 460, 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 148, 321, 460, 414. So, keep reading to learn more.
Given numbers are 148,321,460,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 148,321,460,414 is 16390260.
Find LCM of 148,321,460,414 with Prime Factorization
| 2 | 148, 321, 460, 414 |
| 2 | 74, 321, 230, 207 |
| 3 | 37, 321, 115, 207 |
| 23 | 37, 107, 115, 69 |
| 37, 107, 5, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 23 x 37 x 107 x 5 x 3 = 16390260
Therefore, the lowest common multiple of 148,321,460,414 is 16390260.
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.
148 x 321 x 460 x 414 = 9047423520
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.
148 : 1, 2, 4, 37, 74, 148
321 : 1, 3, 107, 321
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
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 148,321,460,414, is 1.
Now, the common factors can be found like this.
148:2x 2x 37
321:3x 107
460:2x 2x 5x 23
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 2x 2x 3x 23 = 552
Therefore, the value for common factors is 552.
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 = 9047423520/(1x552)
LCM = 9047423520/552
LCM = 16390260
Thus, we can understand that the LCM of 148,321,460,414 is 16390260.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 148, 321, 460, 414
1. What is the LCM of 148, 321, 460, 414?
Answer: LCM of 148, 321, 460, 414 is 16390260.
2. How to calculate the LCM of 148, 321, 460, 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 148, 321, 460, 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}.