LCM of 105, 420, 284, 283, 498
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 420, 284, 283, 498 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 105, 420, 284, 283, 498. So, keep reading to learn more.
Given numbers are 105,420,284,283,498
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,420,284,283,498 is 700441980.
Find LCM of 105,420,284,283,498 with Prime Factorization
| 2 | 105, 420, 284, 283, 498 |
| 2 | 105, 210, 142, 283, 249 |
| 3 | 105, 105, 71, 283, 249 |
| 5 | 35, 35, 71, 283, 83 |
| 7 | 7, 7, 71, 283, 83 |
| 1, 1, 71, 283, 83 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 1 x 1 x 71 x 283 x 83 = 700441980
Therefore, the lowest common multiple of 105,420,284,283,498 is 700441980.
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.
105 x 420 x 284 x 283 x 498 = 1765113789600
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.
105 : 1, 3, 5, 7, 15, 21, 35, 105
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
284 : 1, 2, 4, 71, 142, 284
283 : 1, 283
498 : 1, 2, 3, 6, 83, 166, 249, 498
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,420,284,283,498, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
420:2x 2x 3x 5x 7
284:2x 2x 71
283:283
498:2x 3x 83
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 3x 5x 7 = 2520
Therefore, the value for common factors is 2520.
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 = 1765113789600/(1x2520)
LCM = 1765113789600/2520
LCM = 700441980
Thus, we can understand that the LCM of 105,420,284,283,498 is 700441980.
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FAQs on LCM of 105, 420, 284, 283, 498
1. What is the LCM of 105, 420, 284, 283, 498?
Answer: LCM of 105, 420, 284, 283, 498 is 700441980.
2. How to calculate the LCM of 105, 420, 284, 283, 498?
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 105, 420, 284, 283, 498.
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}.