LCM of 972, 978, 135, 330, 180
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 972, 978, 135, 330, 180 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 972, 978, 135, 330, 180. So, keep reading to learn more.
Given numbers are 972,978,135,330,180
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 972,978,135,330,180 is 8713980.
Find LCM of 972,978,135,330,180 with Prime Factorization
| 2 | 972, 978, 135, 330, 180 |
| 2 | 486, 489, 135, 165, 90 |
| 3 | 243, 489, 135, 165, 45 |
| 3 | 81, 163, 15, 55, 45 |
| 3 | 27, 163, 5, 55, 15 |
| 5 | 9, 163, 5, 55, 5 |
| 9, 163, 1, 11, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 5 x 9 x 163 x 1 x 11 x 1 = 8713980
Therefore, the lowest common multiple of 972,978,135,330,180 is 8713980.
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.
972 x 978 x 135 x 330 x 180 = 7622989704000
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.
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
978 : 1, 2, 3, 6, 163, 326, 489, 978
135 : 1, 3, 5, 9, 15, 27, 45, 135
330 : 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330
180 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 972,978,135,330,180, is 3.
Now, the common factors can be found like this.
972:2x 2x 3x 3x 3x 3x 3
978:2x 3x 163
135:3x 3x 3x 5
330:2x 3x 5x 11
180:2x 2x 3x 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 3x 3x 3x 3x 3x 3x 5x 5 = 291600
Therefore, the value for common factors is 291600.
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 = 7622989704000/(3x291600)
LCM = 7622989704000/874800
LCM = 8713980
Thus, we can understand that the LCM of 972,978,135,330,180 is 8713980.
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FAQs on LCM of 972, 978, 135, 330, 180
1. What is the LCM of 972, 978, 135, 330, 180?
Answer: LCM of 972, 978, 135, 330, 180 is 8713980.
2. How to calculate the LCM of 972, 978, 135, 330, 180?
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 972, 978, 135, 330, 180.
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}.