LCM of 564, 398, 768
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 564, 398, 768 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 564, 398, 768. So, keep reading to learn more.
Given numbers are 564,398,768
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 564,398,768 is 7183104.
Find LCM of 564,398,768 with Prime Factorization
| 2 | 564, 398, 768 |
| 2 | 282, 199, 384 |
| 3 | 141, 199, 192 |
| 47, 199, 64 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 47 x 199 x 64 = 7183104
Therefore, the lowest common multiple of 564,398,768 is 7183104.
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.
564 x 398 x 768 = 172394496
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.
564 : 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
398 : 1, 2, 199, 398
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 564,398,768, is 2.
Now, the common factors can be found like this.
564:2x 2x 3x 47
398:2x 199
768:2x 2x 2x 2x 2x 2x 2x 2x 3
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 3 = 12
Therefore, the value for common factors is 12.
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 = 172394496/(2x12)
LCM = 172394496/24
LCM = 7183104
Thus, we can understand that the LCM of 564,398,768 is 7183104.
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FAQs on LCM of 564, 398, 768
1. What is the LCM of 564, 398, 768?
Answer: LCM of 564, 398, 768 is 7183104.
2. How to calculate the LCM of 564, 398, 768?
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 564, 398, 768.
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}.