LCM of 420, 407, 294, 905
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 407, 294, 905 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 420, 407, 294, 905. So, keep reading to learn more.
Given numbers are 420,407,294,905
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,407,294,905 is 216580980.
Find LCM of 420,407,294,905 with Prime Factorization
| 2 | 420, 407, 294, 905 |
| 3 | 210, 407, 147, 905 |
| 5 | 70, 407, 49, 905 |
| 7 | 14, 407, 49, 181 |
| 2, 407, 7, 181 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 2 x 407 x 7 x 181 = 216580980
Therefore, the lowest common multiple of 420,407,294,905 is 216580980.
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.
420 x 407 x 294 x 905 = 45482005800
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.
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
407 : 1, 11, 37, 407
294 : 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
905 : 1, 5, 181, 905
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,407,294,905, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
407:11x 37
294:2x 3x 7x 7
905:5x 181
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 5x 7 = 210
Therefore, the value for common factors is 210.
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 = 45482005800/(1x210)
LCM = 45482005800/210
LCM = 216580980
Thus, we can understand that the LCM of 420,407,294,905 is 216580980.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 420, 407, 294, 905
1. What is the LCM of 420, 407, 294, 905?
Answer: LCM of 420, 407, 294, 905 is 216580980.
2. How to calculate the LCM of 420, 407, 294, 905?
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 420, 407, 294, 905.
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}.