LCM of 392, 498, 456, 684
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 392, 498, 456, 684 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 392, 498, 456, 684. So, keep reading to learn more.
Given numbers are 392,498,456,684
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 392,498,456,684 is 5563656.
Find LCM of 392,498,456,684 with Prime Factorization
| 2 | 392, 498, 456, 684 |
| 2 | 196, 249, 228, 342 |
| 2 | 98, 249, 114, 171 |
| 3 | 49, 249, 57, 171 |
| 19 | 49, 83, 19, 57 |
| 49, 83, 1, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 19 x 49 x 83 x 1 x 3 = 5563656
Therefore, the lowest common multiple of 392,498,456,684 is 5563656.
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.
392 x 498 x 456 x 684 = 60888651264
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.
392 : 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
498 : 1, 2, 3, 6, 83, 166, 249, 498
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 392,498,456,684, is 2.
Now, the common factors can be found like this.
392:2x 2x 2x 7x 7
498:2x 3x 83
456:2x 2x 2x 3x 19
684:2x 2x 3x 3x 19
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 2x 3x 3x 19 = 5472
Therefore, the value for common factors is 5472.
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 = 60888651264/(2x5472)
LCM = 60888651264/10944
LCM = 5563656
Thus, we can understand that the LCM of 392,498,456,684 is 5563656.
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FAQs on LCM of 392, 498, 456, 684
1. What is the LCM of 392, 498, 456, 684?
Answer: LCM of 392, 498, 456, 684 is 5563656.
2. How to calculate the LCM of 392, 498, 456, 684?
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 392, 498, 456, 684.
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}.