LCM of 488, 420, 314, 870
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 488, 420, 314, 870 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 488, 420, 314, 870. So, keep reading to learn more.
Given numbers are 488,420,314,870
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 488,420,314,870 is 233295720.
Find LCM of 488,420,314,870 with Prime Factorization
| 2 | 488, 420, 314, 870 |
| 2 | 244, 210, 157, 435 |
| 3 | 122, 105, 157, 435 |
| 5 | 122, 35, 157, 145 |
| 122, 7, 157, 29 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 122 x 7 x 157 x 29 = 233295720
Therefore, the lowest common multiple of 488,420,314,870 is 233295720.
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.
488 x 420 x 314 x 870 = 55990972800
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.
488 : 1, 2, 4, 8, 61, 122, 244, 488
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
314 : 1, 2, 157, 314
870 : 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 488,420,314,870, is 2.
Now, the common factors can be found like this.
488:2x 2x 2x 61
420:2x 2x 3x 5x 7
314:2x 157
870:2x 3x 5x 29
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 5 = 120
Therefore, the value for common factors is 120.
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 = 55990972800/(2x120)
LCM = 55990972800/240
LCM = 233295720
Thus, we can understand that the LCM of 488,420,314,870 is 233295720.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 488, 420, 314, 870
1. What is the LCM of 488, 420, 314, 870?
Answer: LCM of 488, 420, 314, 870 is 233295720.
2. How to calculate the LCM of 488, 420, 314, 870?
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 488, 420, 314, 870.
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}.