LCM of 120, 168, 630, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 120, 168, 630, 678 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 120, 168, 630, 678. So, keep reading to learn more.
Given numbers are 120,168,630,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 120,168,630,678 is 284760.
Find LCM of 120,168,630,678 with Prime Factorization
| 2 | 120, 168, 630, 678 |
| 2 | 60, 84, 315, 339 |
| 2 | 30, 42, 315, 339 |
| 3 | 15, 21, 315, 339 |
| 5 | 5, 7, 105, 113 |
| 7 | 1, 7, 21, 113 |
| 1, 1, 3, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 1 x 1 x 3 x 113 = 284760
Therefore, the lowest common multiple of 120,168,630,678 is 284760.
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.
120 x 168 x 630 x 678 = 8611142400
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.
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
168 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
630 : 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
678 : 1, 2, 3, 6, 113, 226, 339, 678
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 120,168,630,678, is 6.
Now, the common factors can be found like this.
120:2x 2x 2x 3x 5
168:2x 2x 2x 3x 7
630:2x 3x 3x 5x 7
678:2x 3x 113
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 3x 3x 5x 7 = 5040
Therefore, the value for common factors is 5040.
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 = 8611142400/(6x5040)
LCM = 8611142400/30240
LCM = 284760
Thus, we can understand that the LCM of 120,168,630,678 is 284760.
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FAQs on LCM of 120, 168, 630, 678
1. What is the LCM of 120, 168, 630, 678?
Answer: LCM of 120, 168, 630, 678 is 284760.
2. How to calculate the LCM of 120, 168, 630, 678?
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 120, 168, 630, 678.
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}.