LCM of 144, 358, 378, 460
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 144, 358, 378, 460 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 144, 358, 378, 460. So, keep reading to learn more.
Given numbers are 144,358,378,460
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 144,358,378,460 is 62249040.
Find LCM of 144,358,378,460 with Prime Factorization
| 2 | 144, 358, 378, 460 |
| 2 | 72, 179, 189, 230 |
| 3 | 36, 179, 189, 115 |
| 3 | 12, 179, 63, 115 |
| 4, 179, 21, 115 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 4 x 179 x 21 x 115 = 62249040
Therefore, the lowest common multiple of 144,358,378,460 is 62249040.
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.
144 x 358 x 378 x 460 = 8963861760
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.
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
358 : 1, 2, 179, 358
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 144,358,378,460, is 2.
Now, the common factors can be found like this.
144:2x 2x 2x 2x 3x 3
358:2x 179
378:2x 3x 3x 3x 7
460:2x 2x 5x 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 3 = 72
Therefore, the value for common factors is 72.
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 = 8963861760/(2x72)
LCM = 8963861760/144
LCM = 62249040
Thus, we can understand that the LCM of 144,358,378,460 is 62249040.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 144, 358, 378, 460
1. What is the LCM of 144, 358, 378, 460?
Answer: LCM of 144, 358, 378, 460 is 62249040.
2. How to calculate the LCM of 144, 358, 378, 460?
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 144, 358, 378, 460.
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}.