LCM of 667, 378, 460, 642
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 667, 378, 460, 642 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 667, 378, 460, 642. So, keep reading to learn more.
Given numbers are 667,378,460,642
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 667,378,460,642 is 269774820.
Find LCM of 667,378,460,642 with Prime Factorization
| 2 | 667, 378, 460, 642 |
| 3 | 667, 189, 230, 321 |
| 23 | 667, 63, 230, 107 |
| 29, 63, 10, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 23 x 29 x 63 x 10 x 107 = 269774820
Therefore, the lowest common multiple of 667,378,460,642 is 269774820.
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.
667 x 378 x 460 x 642 = 74457850320
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.
667 : 1, 23, 29, 667
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
642 : 1, 2, 3, 6, 107, 214, 321, 642
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 667,378,460,642, is 1.
Now, the common factors can be found like this.
667:23x 29
378:2x 3x 3x 3x 7
460:2x 2x 5x 23
642:2x 3x 107
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 3x 23 = 276
Therefore, the value for common factors is 276.
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 = 74457850320/(1x276)
LCM = 74457850320/276
LCM = 269774820
Thus, we can understand that the LCM of 667,378,460,642 is 269774820.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 667, 378, 460, 642
1. What is the LCM of 667, 378, 460, 642?
Answer: LCM of 667, 378, 460, 642 is 269774820.
2. How to calculate the LCM of 667, 378, 460, 642?
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 667, 378, 460, 642.
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}.