LCM of 498, 315, 288
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 498, 315, 288 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 498, 315, 288. So, keep reading to learn more.
Given numbers are 498,315,288
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 498,315,288 is 836640.
Find LCM of 498,315,288 with Prime Factorization
| 2 | 498, 315, 288 |
| 3 | 249, 315, 144 |
| 3 | 83, 105, 48 |
| 83, 35, 16 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 83 x 35 x 16 = 836640
Therefore, the lowest common multiple of 498,315,288 is 836640.
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.
498 x 315 x 288 = 45178560
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.
498 : 1, 2, 3, 6, 83, 166, 249, 498
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 498,315,288, is 3.
Now, the common factors can be found like this.
498:2x 3x 83
315:3x 3x 5x 7
288:2x 2x 2x 2x 2x 3x 3
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 3 = 18
Therefore, the value for common factors is 18.
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 = 45178560/(3x18)
LCM = 45178560/54
LCM = 836640
Thus, we can understand that the LCM of 498,315,288 is 836640.
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FAQs on LCM of 498, 315, 288
1. What is the LCM of 498, 315, 288?
Answer: LCM of 498, 315, 288 is 836640.
2. How to calculate the LCM of 498, 315, 288?
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 498, 315, 288.
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}.