LCM of 456, 312, 684, 240, 288
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 456, 312, 684, 240, 288 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 456, 312, 684, 240, 288. So, keep reading to learn more.
Given numbers are 456,312,684,240,288
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 456,312,684,240,288 is 355680.
Find LCM of 456,312,684,240,288 with Prime Factorization
| 2 | 456, 312, 684, 240, 288 |
| 2 | 228, 156, 342, 120, 144 |
| 2 | 114, 78, 171, 60, 72 |
| 2 | 57, 39, 171, 30, 36 |
| 3 | 57, 39, 171, 15, 18 |
| 3 | 19, 13, 57, 5, 6 |
| 19 | 19, 13, 19, 5, 2 |
| 1, 13, 1, 5, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 19 x 1 x 13 x 1 x 5 x 2 = 355680
Therefore, the lowest common multiple of 456,312,684,240,288 is 355680.
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.
456 x 312 x 684 x 240 x 288 = 6726346997760
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.
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
12 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 456,312,684,240,288, is 12.
Now, the common factors can be found like this.
456:2x 2x 2x 3x 19
312:2x 2x 2x 3x 13
684:2x 2x 3x 3x 19
240:2x 2x 2x 2x 3x 5
288:2x 2x 2x 2x 2x 3x 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 2x 2x 2x 2x 2x 2x 2x 2x 3x 3x 3x 3x 19 = 1575936
Therefore, the value for common factors is 1575936.
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 = 6726346997760/(12x1575936)
LCM = 6726346997760/18911232
LCM = 355680
Thus, we can understand that the LCM of 456,312,684,240,288 is 355680.
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FAQs on LCM of 456, 312, 684, 240, 288
1. What is the LCM of 456, 312, 684, 240, 288?
Answer: LCM of 456, 312, 684, 240, 288 is 355680.
2. How to calculate the LCM of 456, 312, 684, 240, 288?
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 456, 312, 684, 240, 288.
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}.