LCM of 419, 345, 420, 667
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 419, 345, 420, 667 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 419, 345, 420, 667. So, keep reading to learn more.
Given numbers are 419,345,420,667
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 419,345,420,667 is 117378660.
Find LCM of 419,345,420,667 with Prime Factorization
| 3 | 419, 345, 420, 667 |
| 5 | 419, 115, 140, 667 |
| 23 | 419, 23, 28, 667 |
| 419, 1, 28, 29 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 23 x 419 x 1 x 28 x 29 = 117378660
Therefore, the lowest common multiple of 419,345,420,667 is 117378660.
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.
419 x 345 x 420 x 667 = 40495637700
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.
419 : 1, 419
345 : 1, 3, 5, 15, 23, 69, 115, 345
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
667 : 1, 23, 29, 667
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 419,345,420,667, is 1.
Now, the common factors can be found like this.
419:419
345:3x 5x 23
420:2x 2x 3x 5x 7
667:23x 29
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 5x 23 = 345
Therefore, the value for common factors is 345.
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 = 40495637700/(1x345)
LCM = 40495637700/345
LCM = 117378660
Thus, we can understand that the LCM of 419,345,420,667 is 117378660.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 419, 345, 420, 667
1. What is the LCM of 419, 345, 420, 667?
Answer: LCM of 419, 345, 420, 667 is 117378660.
2. How to calculate the LCM of 419, 345, 420, 667?
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 419, 345, 420, 667.
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}.