LCM of 420, 746, 306, 219, 896
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 746, 306, 219, 896 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, 746, 306, 219, 896. So, keep reading to learn more.
Given numbers are 420,746,306,219,896
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,746,306,219,896 is 18663845760.
Find LCM of 420,746,306,219,896 with Prime Factorization
| 2 | 420, 746, 306, 219, 896 |
| 2 | 210, 373, 153, 219, 448 |
| 3 | 105, 373, 153, 219, 224 |
| 7 | 35, 373, 51, 73, 224 |
| 5, 373, 51, 73, 32 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 5 x 373 x 51 x 73 x 32 = 18663845760
Therefore, the lowest common multiple of 420,746,306,219,896 is 18663845760.
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 746 x 306 x 219 x 896 = 18813156526080
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
746 : 1, 2, 373, 746
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
219 : 1, 3, 73, 219
896 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,746,306,219,896, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
746:2x 373
306:2x 3x 3x 17
219:3x 73
896:2x 2x 2x 2x 2x 2x 2x 7
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 2x 3x 3x 7 = 1008
Therefore, the value for common factors is 1008.
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 = 18813156526080/(1x1008)
LCM = 18813156526080/1008
LCM = 18663845760
Thus, we can understand that the LCM of 420,746,306,219,896 is 18663845760.
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FAQs on LCM of 420, 746, 306, 219, 896
1. What is the LCM of 420, 746, 306, 219, 896?
Answer: LCM of 420, 746, 306, 219, 896 is 18663845760.
2. How to calculate the LCM of 420, 746, 306, 219, 896?
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, 746, 306, 219, 896.
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}.