LCM of 978, 409, 288, 460, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 978, 409, 288, 460, 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 978, 409, 288, 460, 678. So, keep reading to learn more.
Given numbers are 978,409,288,460,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 978,409,288,460,678 is 249505247520.
Find LCM of 978,409,288,460,678 with Prime Factorization
| 2 | 978, 409, 288, 460, 678 |
| 2 | 489, 409, 144, 230, 339 |
| 3 | 489, 409, 72, 115, 339 |
| 163, 409, 24, 115, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 163 x 409 x 24 x 115 x 113 = 249505247520
Therefore, the lowest common multiple of 978,409,288,460,678 is 249505247520.
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.
978 x 409 x 288 x 460 x 678 = 35928755642880
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.
978 : 1, 2, 3, 6, 163, 326, 489, 978
409 : 1, 409
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
678 : 1, 2, 3, 6, 113, 226, 339, 678
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 978,409,288,460,678, is 1.
Now, the common factors can be found like this.
978:2x 3x 163
409:409
288:2x 2x 2x 2x 2x 3x 3
460:2x 2x 5x 23
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 3 = 144
Therefore, the value for common factors is 144.
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 = 35928755642880/(1x144)
LCM = 35928755642880/144
LCM = 249505247520
Thus, we can understand that the LCM of 978,409,288,460,678 is 249505247520.
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FAQs on LCM of 978, 409, 288, 460, 678
1. What is the LCM of 978, 409, 288, 460, 678?
Answer: LCM of 978, 409, 288, 460, 678 is 249505247520.
2. How to calculate the LCM of 978, 409, 288, 460, 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 978, 409, 288, 460, 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}.