LCM of 240, 456, 612, 816
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 240, 456, 612, 816 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 240, 456, 612, 816. So, keep reading to learn more.
Given numbers are 240,456,612,816
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 240,456,612,816 is 232560.
Find LCM of 240,456,612,816 with Prime Factorization
| 2 | 240, 456, 612, 816 |
| 2 | 120, 228, 306, 408 |
| 2 | 60, 114, 153, 204 |
| 2 | 30, 57, 153, 102 |
| 3 | 15, 57, 153, 51 |
| 17 | 5, 19, 17, 51 |
| 5, 19, 1, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 17 x 5 x 19 x 1 x 3 = 232560
Therefore, the lowest common multiple of 240,456,612,816 is 232560.
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.
240 x 456 x 612 x 816 = 54653460480
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.
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
612 : 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
816 : 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
12 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 240,456,612,816, is 12.
Now, the common factors can be found like this.
240:2x 2x 2x 2x 3x 5
456:2x 2x 2x 3x 19
612:2x 2x 3x 3x 17
816:2x 2x 2x 2x 3x 17
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 17 = 19584
Therefore, the value for common factors is 19584.
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 = 54653460480/(12x19584)
LCM = 54653460480/235008
LCM = 232560
Thus, we can understand that the LCM of 240,456,612,816 is 232560.
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FAQs on LCM of 240, 456, 612, 816
1. What is the LCM of 240, 456, 612, 816?
Answer: LCM of 240, 456, 612, 816 is 232560.
2. How to calculate the LCM of 240, 456, 612, 816?
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 240, 456, 612, 816.
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}.