LCM of 678, 192, 105, 624
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 192, 105, 624 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 678, 192, 105, 624. So, keep reading to learn more.
Given numbers are 678,192,105,624
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,192,105,624 is 9871680.
Find LCM of 678,192,105,624 with Prime Factorization
| 2 | 678, 192, 105, 624 |
| 2 | 339, 96, 105, 312 |
| 2 | 339, 48, 105, 156 |
| 2 | 339, 24, 105, 78 |
| 3 | 339, 12, 105, 39 |
| 113, 4, 35, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 113 x 4 x 35 x 13 = 9871680
Therefore, the lowest common multiple of 678,192,105,624 is 9871680.
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.
678 x 192 x 105 x 624 = 8529131520
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.
678 : 1, 2, 3, 6, 113, 226, 339, 678
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
105 : 1, 3, 5, 7, 15, 21, 35, 105
624 : 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,192,105,624, is 3.
Now, the common factors can be found like this.
678:2x 3x 113
192:2x 2x 2x 2x 2x 2x 3
105:3x 5x 7
624:2x 2x 2x 2x 3x 13
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 3 = 288
Therefore, the value for common factors is 288.
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 = 8529131520/(3x288)
LCM = 8529131520/864
LCM = 9871680
Thus, we can understand that the LCM of 678,192,105,624 is 9871680.
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FAQs on LCM of 678, 192, 105, 624
1. What is the LCM of 678, 192, 105, 624?
Answer: LCM of 678, 192, 105, 624 is 9871680.
2. How to calculate the LCM of 678, 192, 105, 624?
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 678, 192, 105, 624.
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}.