LCM of 342, 192, 648, 120
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 342, 192, 648, 120 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 342, 192, 648, 120. So, keep reading to learn more.
Given numbers are 342,192,648,120
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 342,192,648,120 is 492480.
Find LCM of 342,192,648,120 with Prime Factorization
| 2 | 342, 192, 648, 120 |
| 2 | 171, 96, 324, 60 |
| 2 | 171, 48, 162, 30 |
| 3 | 171, 24, 81, 15 |
| 3 | 57, 8, 27, 5 |
| 19, 8, 9, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 19 x 8 x 9 x 5 = 492480
Therefore, the lowest common multiple of 342,192,648,120 is 492480.
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.
342 x 192 x 648 x 120 = 5106032640
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.
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
648 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 342,192,648,120, is 6.
Now, the common factors can be found like this.
342:2x 3x 3x 19
192:2x 2x 2x 2x 2x 2x 3
648:2x 2x 2x 3x 3x 3x 3
120:2x 2x 2x 3x 5
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 2x 3x 3x 3 = 1728
Therefore, the value for common factors is 1728.
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 = 5106032640/(6x1728)
LCM = 5106032640/10368
LCM = 492480
Thus, we can understand that the LCM of 342,192,648,120 is 492480.
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FAQs on LCM of 342, 192, 648, 120
1. What is the LCM of 342, 192, 648, 120?
Answer: LCM of 342, 192, 648, 120 is 492480.
2. How to calculate the LCM of 342, 192, 648, 120?
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 342, 192, 648, 120.
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}.