LCM of 400, 123, 978, 564, 752
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 400, 123, 978, 564, 752 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 400, 123, 978, 564, 752. So, keep reading to learn more.
Given numbers are 400,123,978,564,752
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 400,123,978,564,752 is 376921200.
Find LCM of 400,123,978,564,752 with Prime Factorization
| 2 | 400, 123, 978, 564, 752 |
| 2 | 200, 123, 489, 282, 376 |
| 2 | 100, 123, 489, 141, 188 |
| 2 | 50, 123, 489, 141, 94 |
| 3 | 25, 123, 489, 141, 47 |
| 47 | 25, 41, 163, 47, 47 |
| 25, 41, 163, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 47 x 25 x 41 x 163 x 1 x 1 = 376921200
Therefore, the lowest common multiple of 400,123,978,564,752 is 376921200.
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.
400 x 123 x 978 x 564 x 752 = 20408021452800
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.
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
123 : 1, 3, 41, 123
978 : 1, 2, 3, 6, 163, 326, 489, 978
564 : 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
752 : 1, 2, 4, 8, 16, 47, 94, 188, 376, 752
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 400,123,978,564,752, is 1.
Now, the common factors can be found like this.
400:2x 2x 2x 2x 5x 5
123:3x 41
978:2x 3x 163
564:2x 2x 3x 47
752:2x 2x 2x 2x 47
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 2x 3x 3x 47 = 54144
Therefore, the value for common factors is 54144.
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 = 20408021452800/(1x54144)
LCM = 20408021452800/54144
LCM = 376921200
Thus, we can understand that the LCM of 400,123,978,564,752 is 376921200.
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FAQs on LCM of 400, 123, 978, 564, 752
1. What is the LCM of 400, 123, 978, 564, 752?
Answer: LCM of 400, 123, 978, 564, 752 is 376921200.
2. How to calculate the LCM of 400, 123, 978, 564, 752?
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 400, 123, 978, 564, 752.
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}.